The in uence of composition, processing and temperature on

The influence of composition, processingand temperature on the Young’s modulusof elasticity of carbon-bonded refractories

By the Faculty of Maschinenbau, Verfahrens- und Energietechnik

of the Technische Universitat Bergakademie Freiberg

approved

Thesis

to attain the academic degree of

Doktor - Ingenieur

(Dr. - Ing.)

submitted by Dipl. - Ing. Joern Werner

born on the 1st December 1983 in Berlin

Assessor: Prof. Dr.-Ing. habil. Christos G. AnezirisProf. Dr.-Ing. habil. Horst Biermann

Date of the award:Freiberg, 3rd November 2014

Versicherung

Hiermit versichere ich, dass ich die vorliegende Arbeit ohne unzulassige Hilfe Dritter

und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe; die aus

fremden Quellen direkt oder indirekt ubernommenen Gedanken sind als solche kenntlich

gemacht.

Die Hilfe eines Promotionsberaters habe ich nicht in Anspruch genommen. Weitere Per-

sonen haben von mir keine geldwerten Leistungen fur Arbeiten erhalten, die nicht als

solche kenntlich gemacht worden sind. Die Arbeit wurde bisher weder im Inland noch

im Ausland in gleicher oder ahnlicher Form einer anderen Prufungsbehorde vorgelegt.

03. November 2014 Dipl. - Ing. Joern Werner

Declaration

I hereby declare that I completed this work without any improper help from a third

party and without using any aids other than those cited. All ideas derived directly or

indirectly from other sources are identified as such.

I did not seek the help of a professional doctorate-consultant. Only those persons identi-

fied as having done so received any financial payment from me for any work done for me.

This thesis has not previously been published in the same or a similar form in Germany

or abroad.

3rd November 2014 Dipl. - Ing. Joern Werner

v

Acknowledgement

This work was carried out at the Institute of Ceramics, Glass and Construction Materials

TU Bergakademie Freiberg.

First of all I would like to thank my supervisor Prof. Dr.-Ing.-habil. Christos G. Aneziris

for the opportunity to carry out that study and for the dialogues. Furthermore, I would

like to thank all my colleagues at the institute for the discussions and additional support.

A special thanks I would like to address to Prof. Jose de Anchieta Rodrigues from the

Federal University of Sao Carlos who supported my work from the very beginning with

fruitful conversations.

Many thanks to my family and my friends who always supported me and without them

I would not have been able to accomplish that work.

Finally, I would like to gratefully acknowledge the German Research Foundation (DFG)

for supporting the Collaborative Research Center CRC 920 and the integrated MGK for

offering a great variety of further education possibilities.

vii

Contents

List of Symbols xi

List of Figures xiii

List of Tables xix

1. Introduction 1

2. State of the art 3

2.1. Elasticity of ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.2. Microstructural dependence of elastic moduli . . . . . . . . . . . . 5

2.1.3. High temperature dependence of elastic moduli . . . . . . . . . . . 8

2.2. Measurement of elastic moduli . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1. Quasi-static method . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2. Dynamic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Ultrasonic wave velocity method . . . . . . . . . . . . . . . . . . . 13

Resonance frequency method . . . . . . . . . . . . . . . . . . . . . 15

2.2.3. Comparison of static and dynamic methods . . . . . . . . . . . . . 18

2.3. Thermal shock resistance assessement for refractories . . . . . . . . . . . . 20

2.4. Carbon-bonded alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.1. Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3. Materials and methods 27

3.1. Industry related compositions . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1. Variation of the binder content, bonding system and maximum

particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2. Variation of the pyrolysis temperature . . . . . . . . . . . . . . . . 30

3.1.3. Variation of the molding pressure for porosity variation . . . . . . 30

3.2. Reference compositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

viii Contents

3.3. Carbon-bonded open cell foam structures . . . . . . . . . . . . . . . . . . 32

3.3.1. Filter coating bulk material . . . . . . . . . . . . . . . . . . . . . . 32

3.3.2. Filter structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4. Results and discussion 37

4.1. Industry related compositions - Processing and composition influence on

Young’s modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1. Composition T20 an exemplary carbon-bonded alumina . . . . . . 37

4.1.2. Influence of different binder systems . . . . . . . . . . . . . . . . . 41

4.1.3. Influence of different pyrolysis temperatures . . . . . . . . . . . . . 44

4.1.4. Influence of porosity . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2. Reference compositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2.1. Influence of the maximum alumina particle size and the graphite

content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Room temperature investigation . . . . . . . . . . . . . . . . . . . 59

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

High temperature investigation . . . . . . . . . . . . . . . . . . . . 68

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.2. Influence of the maximum alumina particle size and the carbon

filler type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Comparison of fine graphite (AF) to AF/NFL mix (fine/coarse) . 79

Comparison of coarse graphite (NFL) to AF/NFL mix (fine/coarse) 81

Comparison of carbon black (991) to AF/NFL mix (fine/coarse) . 81

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3. Young’s modulus of carbon-bonded open cell foam structures . . . . . . . 85

4.3.1. Room temperature observations . . . . . . . . . . . . . . . . . . . 85

4.3.2. High temperature observations . . . . . . . . . . . . . . . . . . . . 87

4.3.3. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5. Experimental errors and error analysis 95

6. Summary and outlook 97

Bibliography 101

Contents ix

A. Appendix 113

A.1. Additional results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.1.1. Influence of graphite content and maximum particle size . . . . . . 113

Room temperature results . . . . . . . . . . . . . . . . . . . . . . . 113

High temperature measurement results . . . . . . . . . . . . . . . . 118

A.1.2. Influence of carbon filler type and maximum particle size . . . . . 129

A.1.3. Young’s modulus of carbon-bonded open cell foam structures . . . 133

xi

List of Symbols

Symbol Units Description

b mm Width of a rectangular bar

cp J K−1 m−3 Heat capacity per volume unit at constant pressure

d mm Diameter of a rod

dmax mm Maximum alumina particle size of an experimental

composition

ff Hz / s−1 Flexural or torsional resonance frequency

ft Hz / s−1 Flexural or torsional resonance frequency

h mm Height of a rectangular bar

l mm Length of a rod or a rectangular bar

m g Mass of a specimen

vl m s−1 Propagation velocity of a longitudinal ultrasonic

wave

vt m s−1 Propagation velocity of a transverse ultrasonic wave

C1 − Geometric constant of proportionality ≈ 1 for open

cell foams

E GPa Young’s modulus

E0 GPa Young’s modulus either at 0 K, 0 porosity or without

cracks

Ead GPa Adiabatic Young’s modulus

ED GPa Dynamically determined Young’s modulus

ER GPa Young’s modulus of a composite according to the

Reuss boundary

ES GPa Young’s modulus of the strut material of an open cell

foam

ESt GPa Statically determined Young’s modulus

ET GPa Isothermal Young’s modulus

xii List of Symbols

EV GPa Young’s modulus of a composite according to the

Voigt boundary

E∗ GPa Young’s modulus of an open cell foam

F N Load in a load deflection experiment

G GPa Modulus of rigidity or shear modulus

Gf J m−2 Specific fracture energy

K GPa Bulk modulus

L mm Distance between the supports in the three point

bending test

P − Pore volume fraction

Q−1 − Damping of a vibration

R K Thermal shock resistance parameters

R′ K Thermal shock resistance parameters

R′′′′ K Thermal shock damage parameters

Rst K Thermal shock damage parameters

T ◦C Temperature

T0 K Temperature equal to 0 K

α K−1 Linear thermal expansion coefficient

β K−1 Volume thermal expansion coefficient

γ − Shear strain

δ − Logarithmic decrement of a vibration

ε − Strain

λ W m−1 K−1 Thermal conductivity

ν − Poisson’s ratio

πP % Porosity (calculated) after pressing

πa % Apparent porosity determined by water immersion

ρb g cm−3 Bulk density

ρt g cm−3 Theoretical density

ρS g cm−3 Density of the strut material of an open cell foam

ρ∗ g cm−3 Density of an open cell foam

σ N/mm2 Tensile stress or materials strength (e.g. in bending)

τ N/mm2 Shear stress

φ − Volume fraction

xiii

List of Figures

2.1. Temperature dependency of Young’s modulus of alumina modeled accord-

ing to equation 2.9, parameters taken from Wachtman et al. [1961] . . . . 8

2.2. Temperature dependency of Young’s modulus of graphite; Illustration

taken from [Mason and Knibbs, 1960] . . . . . . . . . . . . . . . . . . . . 9

2.3. Young’s modulus dependence of composite refractories on the tempera-

ture; Figures taken from [Gault et al., 1985] . . . . . . . . . . . . . . . . 10

2.4. Young’s modulus dependence of cured carbon-bonded magnesia refracto-

ries on the temperature (Cycling from 800 to 1400 ◦C); Figure taken from

[Buchebner et al., 2008] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5. Ultrasonic testing device with plugged sample, transducer and receiver

are above and below the sample . . . . . . . . . . . . . . . . . . . . . . . 14

2.6. The signal converting way of the impulse excitation technique; a 440 Hz

sound signal input is transformated into a frequency spectrum by a fast

Fourier transformation (FFT) algorithm . . . . . . . . . . . . . . . . . . . 15

2.7. Schematic view of impulse excitation setup for a rectangular bar according

to ASTM E1876 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1. Schematic view of the IET-HT setup (Figure originally published in [Werner

et al., 2013]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1. Young’s modulus of elasticity variation versus temperature normalized to

room temperature value E0 for T20 and the oxidation experiment; on the

right the mass change during the oxidation cycle is shown . . . . . . . . . 38

4.2. Young’s modulus of elasticity evolution within the cycling experiment for

T20; Ei is the initial E value before the experiment started, E0 presents

the E value at room temperature after each cycle while ETmax is the

maximum E value after the holding time . . . . . . . . . . . . . . . . . . . 40

xiv List of Figures

4.3. Change of Young’s modulus during the soak time of the resin (T20 and

T20-B10) and Carbores® bonded (T20-C) materials, Ei represents the

initial value of E at 1450 ◦C . . . . . . . . . . . . . . . . . . . . . . . . . . 40


room temperature value E0 for 6 and 10 wt % resin bonded material; on

the right the thermal expansion is shown . . . . . . . . . . . . . . . . . . . 42


room temperature value E0 for resin and Carbores® bonded materials;

on the right the thermal expansion is shown . . . . . . . . . . . . . . . . . 43

4.6. Elastic and physical properties of the T20-B10 samples treated at pyrolysis

temperatures of 700 ◦C, 1000 ◦C and 1400 ◦C; measured at room temperature 45

4.7. Young’s modulus and thermal expansion measurements up to 1450 ◦C for

the composition T20-B10 at different pyrolysis temperatures . . . . . . . 46

4.8. Effect of molding pressure on the apparent porosity, bulk density, Young’s

modulus and shear modulus at room temperature . . . . . . . . . . . . . . 47

4.9. Young’s modulus E plotted versus pore volume fraction P including the

linear regression model (solid line), the Spriggs approach Spriggs [1961]

(dotted line) and the Phani model [Phani and Niyogi, 1986] (dashed line)

fitted to the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.10. Young’s modulus variation versus temperature and normalized to room

temperature value E0 for the tested porosity levels . . . . . . . . . . . . . 49

4.11. A summarizing model of the assumed microstructural changes within the

carbon-bonded alumina during a measurement of E(T ) based on theories

proposed earlier by several authors [Buchebner et al., 2008; Li and Rigaud,

1993; Franklin and Tucker, 1995; Hampel, 2010] . . . . . . . . . . . . . . 52

4.12. Thermal expansion of T20 (6 wt % resin, 0.6 mm alumina particle size

and 20 wt % graphite) is shown, the dotted lines are approximations of

the coefficient of thermal expansion below and above the former pyrolysis

temperature; In the table on the right the expansion coefficients above and

below the former pyrolysis temperature of the investigated compositions

are shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.13. Measured Young’s modulus E plotted versus temperature T at different

porosity levels P compared to the introduced model (solid line) . . . . . . 58

4.14. Effect of the graphite content and maximum particle size (0.045 mm to

3 mm) on the apparent porosity after the pressing of the reference com-

positions, the dotted horizontal lines represent the confidence levels . . . . 60

List of Figures xv


3 mm) on the apparent porosity after the pyrolysis of the reference com-

positions, the dotted horizontal lines represent the confidence levels . . . . 61


3 mm) on the bulk density of the reference compositions, the dotted hor-

izontal lines represent the confidence levels . . . . . . . . . . . . . . . . . . 62


3 mm) on the Young’s modulus of the reference compositions, the dotted

horizontal lines represent the confidence levels, the confidence plot in (c)

might support the interpretation of the interaction effect found in a) . . . 63


3 mm) on the shear modulus of the reference compositions, the dotted

horizontal lines represent the confidence levels . . . . . . . . . . . . . . . . 64


3 mm) on the Poisson’ ratio of the reference compositions, the dotted

horizontal lines represent the confidence levels . . . . . . . . . . . . . . . . 64


3 mm) on the Damping of the reference compositions, the dotted horizon-

tal lines represent the confidence levels . . . . . . . . . . . . . . . . . . . . 64

4.21. Calculated HS-bounds compared to the measured E of the reference com-

positions; in (c) the calculated b parameter according to Spriggs in de-

pendence on the maximum particle size is shown . . . . . . . . . . . . . . 67

4.22. Young’s modulus and thermal expansion measurement up to 1450 ◦C of

the 0.045 mm composition . . . . . . . . . . . . . . . . . . . . . . . . . . . 69


the 1 mm composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71


the 3 mm composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.25. Young’s modulus change after the high temperature measurement in de-

pendence on the maximum particle size and graphite content; where Ea

represents E after the measurement and Ei before, both at room temper-

ature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.26. Young’s modulus measurement up to 1450 ◦C sorted by graphite content . 77

xvi List of Figures

4.27. Effect of the carbon filler type (AF) and the maximum particle size

(0.045 mm to 3 mm) on the Apparent porosity and bulk density of the

reference compositions, the dotted horizontal lines represent the confi-

dence levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.28. Effect of the carbon filler type (AF) and the maximum particle size

(0.045 mm to 3 mm) on the Young’s and shear modulus and Poisson’s

ratio of the reference compositions, the dotted horizontal lines represent

the confidence levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.29. Effect of the carbon filler type (NFL) and the maximum particle size

(0.045 mm to 3 mm) on the Apparent porosity and bulk density of the ref-

erence compositions, the dotted horizontal lines represent the confidence

levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.30. Effect of the carbon filler type (NFL) and the maximum particle size




4.31. Effect of the carbon filler type (991) and the maximum particle size

(0.045 mm to 3 mm) on the Apparent porosity and bulk density of the

reference compositions, the dotted horizontal lines represent the confi-

dence levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.32. Effect of the carbon filler type (991) and the maximum particle size




4.33. Influence of the Carbores® content on the apparent porosity after the

pressing / pyrolysis, on the Young’s and shear modulus of a filter bulk

material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.34. Young’s modulus of the bulk and foam material (20 wt % Carbores® con-

tent) in dependence on the porosity; Models found in the literature were

fitted against the experimental data to analyze their applicability for this

composite material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.35. Influence of the temperature on the Young’s modulus and linear change of

the bulk material and filter structures which were pyrolyzed at 800 ◦C; the

Young’s modulus dependent on the temperature of alumina is shown at

the bottom for a comparison of the nonlinear decrease of E above 1200 ◦C

of the alumina and the carbon-bonded alumina . . . . . . . . . . . . . . . 89

List of Figures xvii

A.1. Effect of the graphite content and maximum particle size on the porosity

after pressing, apparent porosity and bulk density after pyrolysis at room

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.2. Effect of the graphite content and maximum particle size on the Young’s

modulus, shear modulus and Poisson’s ratio at room temperature . . . . . 114

A.3. Effect of the graphite content and maximum particle size on the damping

behavior and change in length of the sample at room temperature . . . . 114

A.4. Effect of the carbon filler type and maximum particle size on the porosity

after pressing, apparent porosity and bulk density after pyrolysis at room

temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.5. Effect of the carbon filler type and maximum particle size on the Young’s

modulus, shear modulus and Poisson’s ratio at room temperature . . . . . 129

A.6. Effect of the carbon filler type and maximum particle size on the damping

behavior and change in length of the sample at room temperature . . . . 130

xix

List of Tables

2.1. Elastic properties of ceramic materials, taken from Salmang and Scholze

[2007]; Pierson [1997]; McKee [1973] . . . . . . . . . . . . . . . . . . . . . 4

2.2. Models describing E(P ) found in the literature; m, b and c are parameters

to be fitted empirically, E∗ and ρ∗ are the properties of the foam . . . . . 7

2.3. Typical properties of glassy carbon derived from polymer precursors; Ta-

ble taken from McKee [1973] . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1. Industry related compositions . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2. Reference compositions; the composition name can be read as follows:

T(abular alumina of the maximum particle size) - Y - ( mm and of a graphite

content of)X(wt %) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3. Filter coating bulk material composition according to Emmel and Aneziris

[2012]; Three different levels of porosity were obtained by introducing a

pore forming agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4. Filter coating bulk material composition with Carbores® P variation to

study its influence on the elastic properties . . . . . . . . . . . . . . . . . 34

4.1. Apparent porosity πa and E of the investigated compositions at room

temperature; mean values and the confidence interval for α = 0.05 are

shown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2. Mass loss, change of apparent porosity (difference of initial and end value;

πia − πea) apparent porosity and Young’s modulus at room temperature

after the measurement cycles . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3. Results of the pairwise Student’s t-test (adjusted p-value according to

the Holm-Bonferroni method [Holm, 1979]) for the binder influence on

the high temperature measurement of E up to 1450 ◦C; for each pair a

p-value is shown, p < 0.05 indicates a significant difference . . . . . . . . . 44

xx List of Tables

4.4. Results of the Tukey range test with a p-value of 0.05 for the different

pyrolysis temperatures and response values (E, G, ν, πa and ρb); the

values tested were evaluated at room temperature, p < 0.05 indicates

significant differences between the tested pair . . . . . . . . . . . . . . . . 45

4.5. Results of the pairwise Student’s t-test (adjusted p-value according to the

Holm-Bonferroni method [Holm, 1979]) for the porosity influence on the

high temperature measurement of E up to 1025 ◦C; for each pair a p-value

is shown, p < 0.05 indicates a significant difference . . . . . . . . . . . . . 50

4.6. Model functions and the obtained model parameters for the experimental

E(P ) data; E0 represents the Young’s modulus at zero porosity; z, m and

b are empirical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.7. The factorial design for the investigation of the influence of graphite con-

tent and maximum particle size on the elastic and additional properties . 59

4.8. Results of the pairwise Student’s t-test (adjusted p-value according to the

Holm-Bonferroni method [Holm, 1979]) for the graphite content influence

on the soak time behavior of E for the 1 mm compositions; for each pair

a p-value is shown, p < 0.05 indicates a significant difference . . . . . . . . 72

4.9. Results of the multiple comparison of means ad-hoc test (Tukey-HSD) for

the graphite content influence on the retained porosity and mass loss after

a high temperature measurement for the 0.045 mm compositions; for each

pair a p-value is shown, p < 0.05 indicates a significant difference . . . . . 75

4.10. Coefficients of thermal expansion below and above the pyrolysis temper-

ature of 1000 ◦C in dependence on the graphite content and maximum

particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.11. The factorial design for the investigation of the influence of carbon filler

type and maximum particle size on the elastic and additional properties,

the used filler types were AF = fine natural graphite, NFL = coarse

natural graphite, CB = carbon black and Mix = 1:1 AF/NFL . . . . . . 79

4.12. Results of the Tukey range test with a p-value of 0.05 for the different

Carbores® contents and response values (E, G); the values tested were

evaluated at room temperature, p < 0.05 indicates significant differences

between the tested pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.13. Estimates of the model fits on the experimental data of E(P ) for the

carbon-bonded bulk and foam material (20 wt % Carbores® content), p <

0.05 indicates significance of the estimates . . . . . . . . . . . . . . . . . . 87

List of Tables xxi

4.14. Absolute Young’s modulus values of the bulk material and the filter struc-

ture before the high temperature measurement (pyrolyzed at 800 ◦C) . . . 88

A.1. ANOVA statistic for the factors graphite content and maximum particle

size on the porosity after pressing (PP) and after the pyrolysis (AP), as

well as for the bulk density (BD) . . . . . . . . . . . . . . . . . . . . . . . 113

A.2. ANOVA summary of the Young’s modulus in dependence on the factors

A - graphite content and B - maximum particle size as well as on their

interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

A.3. ANOVA summary of the shear modulus in dependence on the factors


interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A.4. ANOVA summary of the Poisson’s ratio in dependence on the factors


interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A.5. ANOVA summary of the damping in dependence on the factors A -

graphite content and B - maximum particle size as well as on their in-

teraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A.6. ANOVA summary of the apparent porosity in dependence on the factors


interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A.7. ANOVA summary of the bulk density in dependence on the factors A

- graphite content and B - maximum particle size as well as on their

interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A.8. ANOVA summary of the porosity after pressing in dependence on the

factors A - graphite content and B - maximum particle size as well as on

their interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A.9. ANOVA summary of the linear change in length of the samples after

the pyrolysis in dependence on the factors A - graphite content and B -

maximum particle size as well as on their interaction . . . . . . . . . . . . 117

A.10.ANOVA summary of the Young’s modulus from room temperature to

1450◦C of the 0.045 mm compositions in dependence on the factors B -

graphite content and D - temperature as well as on their interaction . . . 118

xxii List of Tables

A.11.Results of the pairwise Student’s t-test (adjusted p-value according to the

Holm-Bonferroni method [Holm, 1979]) of the temperature influence on

E for the 0.045 mm compositions at heating; for each pair a p-value is

shown, p < 0.05 indicates a significant difference . . . . . . . . . . . . . . 119

A.12.ANOVA summary of the Young’s modulus from 1450◦C to room tem-

perature of the 0.045 mm compositions in dependence on the factors B -

graphite content and D - temperature as well as on their interaction . . . 119



E for the 0.045 mm compositions at cooling; for each pair a p-value is

shown, p < 0.05 indicates a significant difference . . . . . . . . . . . . . . 120

A.14.ANOVA summary of the Young’s modulus during the soak time of the

0.045 mm compositions in dependence on the factors B - graphite content

and D - time as well as on their interaction . . . . . . . . . . . . . . . . . 120


Holm-Bonferroni method [Holm, 1979]) of the graphite content influence

on the soak time behavior of E for the 0.045 mm compositions; for each

pair a p-value is shown, p < 0.05 indicates a significant difference . . . . . 121


1450◦C of the 3 mm compositions in dependence on the factors B - graphite

content and D - temperature as well as on their interaction . . . . . . . . 121



E for the 3 mm compositions at heating; for each pair a p-value is shown,

p < 0.05 indicates a significant difference . . . . . . . . . . . . . . . . . . . 122

A.18.ANOVA summary of the Young’s modulus from 1450◦C to room temper-

ature of the 3 mm compositions in dependence on the factors B - graphite




E for the 3 mm compositions at cooling; for each pair a p-value is shown,



3 mm compositions in dependence on the factors B - graphite content and

D - time as well as on their interaction . . . . . . . . . . . . . . . . . . . . 123

List of Tables xxiii






1450◦C of the 1 mm compositions in dependence on the factors B - graphite




E for the 1 mm compositions at heating; for each pair a p-value is shown,


A.24.ANOVA summary of the Young’s modulus from 1450◦C to room temper-

ature of the 1 mm compositions in dependence on the factors B - graphite



1 mm compositions in dependence on the factors B - graphite content and

D - time as well as on their interaction . . . . . . . . . . . . . . . . . . . . 126





A.27.ANOVA summary of the Young’s modulus in dependence on the factors

A - particle size and B - graphite content as well as on their interaction

after the high temperature measurement . . . . . . . . . . . . . . . . . . . 127

A.28.ANOVA summary of the mass loss in dependence on the factors A - par-

ticle size and B - graphite content as well as on their interaction after the

high temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . 127

A.29.ANOVA summary of the porosity change in dependence on the factors A

- particle size and B - graphite content as well as on their interaction after

the high temperature measurement . . . . . . . . . . . . . . . . . . . . . . 128

A.30.ANOVA summary of the Young’s modulus in dependence on the factors

A - carbon filler type and B - maximum particle size as well as on their

interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

A.31.ANOVA summary of the shear modulus in dependence on the factors A

- carbon filler type and B - maximum particle size as well as on their

interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

xxiv List of Tables

A.32.ANOVA summary of the Poisson’s ratio in dependence on the factors A


interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.33.ANOVA summary of the damping in dependence on the factors A - carbon

filler type and B - maximum particle size as well as on their interaction . 131

A.34.ANOVA summary of the apparent porosity in dependence on the factors

A - carbon filler type and B - maximum particle size as well as on their

interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

A.35.ANOVA summary of the bulk density in dependence on the factors A


interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A.36.ANOVA summary of the porosity after pressing in dependence on the

factors A - carbon filler type and B - maximum particle size as well as on

their interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A.37.ANOVA summary of the linear change in length of the samples after the

pyrolysis in dependence on the factors A - carbon filler type and B -

maximum particle size as well as on their interaction . . . . . . . . . . . . 132

A.38.ANOVA summary of the porosity after the pressing in dependence on the

factor A - Carbores® content . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.39.Results of the Tukey range test with a p-value of 0.05 for the influence

of the different Carbores® contents on the apparent porosity after the

pressing; the values tested were evaluated at room temperature, p < 0.05

indicates significant differences between the tested pair . . . . . . . . . . . 133

A.40.ANOVA summary of the porosity after the pyrolysis in dependence on

the factor A - Carbores® content . . . . . . . . . . . . . . . . . . . . . . . 134

A.41.Results of the Tukey range test with a p-value of 0.05 for the influence

of the different Carbores® contents on the porosity after the pyrolysis;

the values tested were evaluated at room temperature, p < 0.05 indicates

significant differences between the tested pair . . . . . . . . . . . . . . . . 134

1

1. Introduction

Refractory materials are of major interest for almost all industries. There are applica-

tions in primary industries like metallurgy (e.g. lining in iron and non-iron metallurgy)

and energy industry (e.g. lining for fossil fuel power plants and fuel rods in nuclear

power plants) [Semler, 2014; Lee, 2012]. Besides, there are also numerous applications

in high technology industries like aerospace industry and automotive industry. They can

be found in the thermal protection for space shuttles, in particle filters for cars and in

rotors, blades and rings for gas turbines [Pierson, 1997; Paul et al., 2012]. For the design

of these products structural information of the used materials is essential.

Therefore, mechanical, thermal and corrosion properties have to be provided by material

scientists. Especially for high temperature application it is necessary to consider the

material reaction on temperature changes. Opening and closing of a furnace during

service, start and stop of turbines or insertion of a Lambda-sonde into a steel melt are

only a few examples of this particular demand [Buchebner et al., 2008; Poirier et al.,

2005].

This behavior is called thermal shock resistance and was firstly addressed by Kingery

[Kingery, 1955] and Hasselman [Hasselman, 1969] in a fracture mechanics view. Kingery

already defined the important material properties to resist a thermal shock as the ma-

terials strength σ, Poisson’s ratio ν, Young’s modulus E and the coefficient of thermal

expansion α. He introduced the so called resistance parameter:

R =(1− ν) · σE · α

(1.1)

which can be regarded as the temperature range ∆T to be resisted by a particular

structure.

Nowadays, these properties are still used as indicators for the thermal shock behavior of

refractory material. However, virtually always they are measured at room temperature

and are used for the thermal shock prediction, although the service temperature range

2 1. Introduction

is mostly at elevated temperatures (e.g. 1200 to 1600◦C for emptying a steel ladle)

[Boccaccini et al., 2008; Aneziris et al., 2007].

Besides the engineering need for exact material properties like Young’s modulus, there is

more information to be gained out of the knowledge of elastic measurements. They are

one of the most direct way of measuring the strength of chemical bonding. Therefore,

the basic data for the calculation of the theoretical strength of crystals can be obtained

by elastic measurements. Furthermore, microstructural analysis of materials can be

carried out according to the results of the measurements. Elastic properties are also used

for the interpretation of wave propagation in the earth as a basis for the fundamental

understanding of its composition [Wachtman, 1969; Patapy et al., 2012; Luz et al., 2013;

Werner et al., 2013].

This work deals with the elastic properties of carbon-bonded refractories. These ma-

terials are widely used for example in steel making. They can be found in linings of

basic oxygen converters or as functional components, like submerged entry nozzles or

mono bloc stoppers in continuous steel making. Knowledge about the room temperature

and high temperature elasticity of this material could enable engineers and scientists to

improve products (complete linings) and materials (composition change). The so called

impulse excitation technique (IET) was used to determine the dynamic elastic constants.

A broad range of factors influencing the microstructure of the material were investigated

(e.g. graphite content, oxide particle size, bonding system, and more). Furthermore, the

application of IET enabled Young’s modulus measurements up to 1450◦C, to address the

lack of data regarding the thermal shock resistance. An overview of the gained informa-

tion will be given. These results will be discussed by comparison to the literature and

well known models from one phase oxide refractories. The results shown and discussed

in this thesis are mainly based on own recent publications [Werner et al., 2013; Werner

and Aneziris, 2013; Werner et al., 2014].

This work should be regarded as a starting point for a deeper understanding of the

microstructure and thermal shock resistance of carbon-bonded refractories.

3

2. State of the art

The following chapter gives an overview of the elastic behavior of carbon-bonded alu-

mina and its relationship to the materials microstructure. Therefore, at first an overview

about the elasticity of ceramics will be given, followed by the microstructure and high

temperature dependence of the elastic moduli. Furthermore, an overview of the elasticity

measurement methods will be provided. Subsequently, the contribution of Young’s mod-

ulus to the calculation and estimation of the thermal shock resistance will be discussed.

Finally, a brief introduction of carbon-bonded alumina as the material investigated in

this study will be given.

2.1. Elasticity of ceramics

2.1.1. Fundamentals

One of the biggest drawbacks of ceramics is their brittle fracture fail behavior. There

is no actual plastic deformation for these materials. Hence, their application is reduced

due to their poor impact resistance [Kingery et al., 1976].

Young’s modulus is closely related to inter atomic bonding forces. By applying a stress

to a crystal lattice, the distance of the atoms can be extended or decreased. This is the

physical origin of Hooke’s law, which the elastic deformation of ceramics follows [Carter

and M.G.Norton, 2007a]. According to Hooke’s law stress is directly proportional to the

strain:

σ = Eε (2.1)

where σ is the stress (tensile), E is Young’s modulus and ε the strain. Similarly, there

is an expression for the shear stress:

τ = Gγ (2.2)

4 2. State of the art

Tab. 2.1.: Elastic properties of ceramic materials, taken from Salmang and Scholze [2007]; Pierson [1997];McKee [1973]

Material E G K νGPa

Al2O3 410 165 255 0.23MgO 310 130 155 0.17ZrO2 190 75 140 0.27Porcelain 76 32 38 0.17Mullite 100 42 56 0.2SiC 480 200 240 0.17Si3N4 295 115 235 0.29Pyrolytic graphite 28− 31 - - -Glassy carbon 14− 33 - - -

where G is the shear modulus or modulus of rigidity and γ the shear strain. The

deformation of a sample due to a tension is connected to a change in thickness. A

characterization of this change is the Poisson’s ratio:

ν = −∆d/d

∆l/l(2.3)

It relates to the elastic moduli as follows:

ν =E

2G− 1 (2.4)

In case of isotropic pressure the elastic response is called bulk modulus K. There are

several equations for the translation of the elastic constants into each other (e.g. E → G).

They can be found for example in Carter and M.G.Norton [2007b].

In Table 2.1 the elastic properties of some ceramic materials are shown. However, these

are virtually theoretical values. Most of these materials are composed of a microstructure

with defects (impurities, pores, grain boundaries). These microstructure variations have

a strong impact on the elasticity.

Also characteristic for ceramic materials is a behavior called an-elasticity. Hereby, the

deformation made to a body is not instantaneously fully recoverable after the removal of

stress [Kingery et al., 1976]. This behavior especially can be observed at high temper-

atures due to grain boundary sliding and softening [Wachtman and Lam, 1959; Chang,

1959]. Moreover, there are several nonlinear effects which can not be explained by

linear elastic theory. Therefore, researchers especially from the field of earth sciences

2.1. Elasticity of ceramics 5

addressed this problem by the introduction of a ”new” material class. Guyer and John-

son [2009] defined the so called ”Nonlinear mesoscopic materials” as materials exhibiting

”extreme/unusual elastic behaviors”.

Materials like ceramics, rocks and soil should be regarded as a mortar-tile system in

which the mortar is the weak bond between the stiff tiles. One of the key conclusions

of this model is that the minor phase (mortar) determines the global properties of the

whole system. For example in a carbon-bonded alumina or magnesia the Young’s mod-

ulus ranges typically from 5 to 80 MPa [Manhart et al., 2005; Buchebner et al., 2008].

Considering the Young’s modulus from Table 2.1, alumina and magnesia show a 3 to

5 times higher E. Apparently the graphite or the pyrolytic carbon obtained from the

binder phase is determining the elastic properties of the composite.

Phenomena related to this material class are well known for refractory materials. For

example the strain relaxation when an applied stress is removed or the shift of resonance

frequency of a bar in dependence on the excitation energy [Pereira et al., 2010, 2011;

Manhart and Harmuth, 2009]. A further example is the hysteresis in stress vs. strain

curves of carbon-bonded materials [Schmitt et al., 2000]. All of these phenomena classify

these materials as nonlinear. Therefore, one has to take into account, that ceramics and

especially refractories do not exhibit exact linear elastic behavior. This is already a

strong field of interest in the refractory research community and there is much work left

to do [Belrhiti et al., 2013].

2.1.2. Microstructural dependence of elastic moduli

Talking about elastic constants one has to take into account that they are always related

to isotropic bodies or more exactly to the materials lattice. However, defects like grain

boundaries, crystalline structure and dislocations have to be considered interpreting

experimental data.

”Therefore, nearly the whole technique of engineering continuum mechanics

is based on semi-intuitively defined effective properties of non-homogeneous

materials.” [Mileiko, 1997]

Most ceramics and virtually all refractories are two or more phase systems (considering

porosity as a phase). For the computation and modeling of these microstructures, the

literature provides a broad range of models and equations. The Young’s modulus of a

composite can be derived from the moduli of the pure elements. Composite constituents


aligned either parallel or perpendicular to an applied stress are the extreme cases. Two

boundary models are established addressing these conditions.

Voigt [1889] assumed layers of each composite phase aligned parallel to the applied

stress. A further assumption is an equal strain level in each constituent, hence the

Young’s modulus of the composite is:

EV = φ2E2 + (1− φ2)E1 (2.5)

where φ2 is the volume fraction of phase two and E2 its Young’s modulus. The second

boundary model by Reuss [1929] assumes a perpendicular alignment of the phases to the

applied stress, which has to be equal in each constituent:

1

ER=φ2E2− 1− φ2

E1(2.6)

A more precise approach was suggested by Hashin and Shtrikman [1963]. This set of

bounds was shown to be the most precise for the determination of the elastic constants of

a composite material with arbitrary phase geometry. However, its validity is limited to

quasi-homogeneous and isotropic materials. For the bulk modulus the Hashin-Shtrikman

bounds are given for K2 > K1 and G2 > G1,

KL = K1 +φ2

1/(K2 −K1) + [3(1− φ2)]/(3K1 + 4G1)(2.7)

KU = K2 +1− φ2

1/(K1 −K2) + 3φ2/(3K2 + 4G2)(2.8)

where KU and KL represent the upper and lower bounds [Kingery et al., 1976; Carter

and M.G.Norton, 2007b]. Considering the composite nature of carbon-bonded alumina,

these models will be discussed further in results and discussions. Reducing the amount

of the second phase to zero would result in a model considering the porosity. In this case

Young’s modulus of the composite will be decreased remarkably (E2 = 0), according to

the introduced models.

There can be found a tremendous amount of models for E(P ) in the literature, either

analytic or empirical. MacKenzie [1950] first addressed the problem of porosity in a

solid body under the assumption of spherical pores. Coble and Kingery [1956] compared

experimental results with MacKenzies model. It appeared to be valid for a porosity

range of 0− 0.5 pore volume fraction.


Tab. 2.2.: Models describing E(P ) found in the literature; m, b and c are parameters to be fittedempirically, E∗ and ρ∗ are the properties of the foam

Model Reference

E = E0e−bP Spriggs [1961]

E = E0(1− P )m Phani and Niyogi [1986]

E = E0(1− P 2)

1 + (c−1 − 1)PNielsen [1984]

E∗

ES= C1

(ρ∗

ρS

)2

Gibson and Ashby [1997] for open cell foams

In the early 1960s several researchers found empirical models for the relationship of

Young’s modulus on the porosity. However, none of them recognized the pore shape as

an influencing factor [Spriggs, 1961; Spriggs et al., 1962; Knudsen, 1962]. These models

can basically be described as an exponential dependency of E on P as can be seen in

Table 2.2. However, this equation does not meet the boarder conditions P = 0→ E = E0

and P = 1→ E = 0 respectively.

Therefore, Nielsen [1984] and Phani and Niyogi [1986] suggested two different models.

These satisfy the boundary conditions declared above and could be applied therefore in

a broader range of porosity. Nielsen [1984] also took the influence of the pore shape

into account as he introduced the shape factor c in his equation (see Table 2.2). More

recent works improved this approach by adding several pore shape and orientation factors

[Andersson, 1996; Boccaccini and Boccaccini, 1997].

The applicability of these models strongly depends on the porosity range. For reasonable

small porosity (0 < P < 0.5) the exponential relationship matches the experimental data

quite well. However, for porosity been higher than 0.5 other approaches have to be taken

into account. As mentioned Phani and Niyogi [1986] proposed a power function for this

correlation. Furthermore, Gibson and Ashby [1997] proposed and summarized models

for cellular solids. They defined E as a function of relative density of the foam and

the Young’s modulus of its bulk material. In terms of open cell foams, which were

investigated within this thesis, they proposed a model to be found in Table 2.2. Recent

studies proved the validity of this model by experimental and analytic means [Knackstedt

et al., 2005; Zhang et al., 2012; Bourret et al., 2013]. Gibson and Ashby [1997] suggested

a value of approximately one for the geometric constant of proportionality C1.

A further microstructural influence on E are microcracks. Their role in terms of crack

propagation will be discussed in subsection 2.3. Stiffler and Hasselman [1983] assumed

microcracks as extremely thin inclusions of zero stiffness. They proposed a model to


0 200 400 600 800 100032

033

034

035

036

037

0

Temperature / K

E /

GP

a

Fig. 2.1.: Temperature dependency of Young’s modulus of alumina modeled according to equation 2.9,parameters taken from Wachtman et al. [1961]

compute the shear modulus of microcracked materials, in the form of the Hashin and

Shtrikman [1963] equation introduced earlier. So microcracks can be regarded as a single

phase in a composite or as porosity in terms of elasticity.

It was shown that the elastic properties of ceramics are strongly related to its crystal

lattice as well as to its microstructure. Several models were introduced to give a brief

overview of the existing prediction possibilities.

2.1.3. High temperature dependence of elastic moduli

Due to the mentioned relationship between the crystal lattice and the elastic properties

of ceramics, one will expect a strong dependence of them on the temperature. The

increase of kinetic energy due to a temperature increase contributes to an extension of the

atomic distance. Hence, Young’s modulus should decrease with increasing temperature.

Several studies confirmed this relationship for one phase oxide ceramics [Schwartz, 1952;

Wachtman and Lam, 1959; Spriggs et al., 1964; Soga and Anderson, 1966; Gerlich and

Fisher, 1969]. Wachtman et al. [1961] suggested a model for this relationship which

satisfies the linear decrease of E at high temperatures as well as the zero slope area at

low temperatures (see Figure 2.1 as well):

E = E0 −BTexp(−T0/T ) (2.9)


Fig. 2.2.: Temperature dependency of Young’s modulus of graphite; Illustration taken from [Mason andKnibbs, 1960]

E0 represents Young’s modulus at 0 K and B is a material dependent constant. However,

it was also observed that Young’s modulus decreases nonlinear at higher temperatures

(depending on the material e.g. ∼ 1000 ◦C for alumina). There was no such behavior for

single crystals (e.g. ruby) found. Therefore, this nonlinear decrease in polycrystalline

oxide ceramics was attributed to a grain boundary slip [Wachtman and Lam, 1959;

Chang, 1959].

Mason and Knibbs [1960] investigated the high temperature Young’s modulus of graphite

(see Figure 2.2) and found an increase instead of the expected decrease for E(T ). They

attributed their result mainly to the strong expansion of the c-axes of graphite crystals.

Thus, voids in the material could be filled resulting in a stiffening effect. They also

reported a hysteresis effect during cooling and explained it with a plastic yielding due to

a suppressed expansion of overcrowding neighbor crystals. This is of important interest

for this study, since graphite is a main constituent of carbon-bonded refractories.

For composite materials and for materials undergoing phase transformations during heat-

ing or cooling, the relationship E(T ) is mostly not linear. Gault et al. [1985] showed this


(a) Aliumina-zirconia-glassy phase composite(AZ)

(b) Alumina-mullite-zirconia composite (AMZ)

(c) Carbon-bonded alumina (CBA)

Fig. 2.3.: Young’s modulus dependence of composite refractories on the temperature; Figures taken from[Gault et al., 1985]

nonlinear E(T ) behavior in their study. They investigated an alumina-mullite-zirconia

composite (AMZ), an alumina-zirconia-silica composite (AZ), an alumina-chromium(III)oxide

(AC) and a carbon-bonded alumina (CBA).

Besides the AC composite, which exhibited almost exact linear behavior, all composites

showed nonlinear behavior. This behavior was attributed to microstructural changes

during heating and cooling. For the zirconia containing composition there is a phase

transformation from the monoclinic to the tetragonal crystal system, which is the denser

one. They reported an increase of E in the temperature range from 950 to 1250 ◦C

(shown in Figure 2.3a) and correlated this to dilatometry measurements showing the

phase transformation in the same temperature range. However, a densification of one

phase might also contribute to an increase in porosity of the composite, resulting in a

lower E. Fogaing et al. [2006] showed a decreasing effect of this phase transformation

for pure zirconia. Hence, the conclusion of Gault et al. [1985] regarding the observed

increase of E might not be entirely correct. This stiffening effect could also be attributed

to a thermal expansion mismatch of the constituents (zirconia, alumina, glassy phase).

As described for graphite above, this could contribute to a void closing and therefore to

an increase of E.

The E(T ) behavior of the alumina-mullite-zirconia composite (AMZ) is quite comparable

2.2. Measurement of elastic moduli 11

to AZ with an increase up to 1000 ◦C (see Figure 2.3b). A proper explanation for this

behavior was not given by the authors. They attributed the hysteresis between cooling

and heating to either the phase transformation in zirconia or a microcrack closure.

Moreover, the results for the carbon-bonded alumina were not explained properly by

the authors. They attributed the ”unstable and markedly irreversible increase” during

heating to the carbon and/or to other elements, such as silicon. This conclusion reveals

a main drawback of this study; the lack of information about the material they used.

There was no hint regarding the initial condition of this material at the beginning of the

measurements. Especially, the condition of the carbon phase (cured or already pyrolysed)

would be of interest for the interpretation of these results.

A more recent study from Baudson et al. [1999] about carbon-bonded magnesia revealed

similar results. The samples were pretreated in a pyrolysis up to 1000 ◦C in a CO

atmosphere. They found a strong increase of E above 1100 ◦C and attributed this to

a bridging of the magnesia particles. Furthermore, they revealed an oxidation of the

pyrolytic carbon derived from the resin in the temperature range from 600 to 800 ◦C.

Manhart et al. [2005] as well as Buchebner et al. [2008] showed the transformation of resin

and pitch into pyrolytic carbon in terms of carbon-bonded magnesia from 25 to 1500 ◦C.

They observed a decrease of E from 350 to 600 ◦C. The overall amount of this decrease

is influenced by the residual carbon content. This depression is caused by the release

of volatile parts of the resin [Cowlard and Lewis, 1967]. The same was observed for

pitch bonded material. At higher temperatures Young’s modulus is slightly decreased.

Furthermore, Buchebner et al. [2008] performed thermal cycles from 800 to 1400 ◦ at

the in-situ cured samples (see Figure 2.4) to gather information regarding structural

changes within the ladle lining. They observed a hysteresis but reversible behavior.

During cooling E decreased significantly and increased at reheating respectively. In

combination with modulus of rupture measurements they gained information for future

magnesia-carbon brick development and life time prediction.

2.2. Measurement of elastic moduli

In general there are two ways to determine elastic moduli experimentally. They can

be divided into quasi-static and dynamic methods. The terms static and dynamic are

roughly bound to the applied strain rate. The static tests introduce large strains at low

strain rates whereas for dynamic tests the opposite holds. This section will introduce


Fig. 2.4.: Young’s modulus dependence of cured carbon-bonded magnesia refractories on the temperature(Cycling from 800 to 1400 ◦C); Figure taken from [Buchebner et al., 2008]

these methods and discuss their results in terms of comparability and applicability for

engineering purposes [Wolfenden, 1990].

2.2.1. Quasi-static method

According to Hooke’s law, Young’s modulus is the slope of the stress strain curve. Thus,

it should be easy to obtain any elastic constant (E,G,K and ν) out of a load-deflection

test in which the load corresponds to the elastic constants.

For refractory materials the three point bending test is most common for obtaining

tensile stress values. A load is subjected to the center of a bar which is mounted on two

supports. At the load application point, a compression stress can be found while on the

other side of the bar a tensile stress occurs. This outer fiber stress is defined as:

σ =3FL

2bh2(2.10)

where F is the load, L is the distance between the supports, b the width and h the

height of the bar. The Young’s modulus can be calculated according to the following

equation:

E =FL3

4bh3y(2.11)

where y represents the deflection. However, especially for refractory materials there are

also contributions to this deflection of slow crack growth and other nonelastic behaviors.

These effects actually increase y resulting in an underestimation of E due to the samples

apparent bending behavior. Therefore, the determination and interpretation of Young’s

modulus, shear modulus or bulk modulus from mechanical load deflection should be


carried out under consideration of these effects [Bradt, 1993]. Typical standards for

determining the Young’s modulus from the load-deflection curve of refractory materials

are ASTM C469 / C469M, ASTM E111 and DIN EN 843-2.

2.2.2. Dynamic methods

The so called dynamic methods are a nondestructive way to obtain the elastic moduli.

The propagation of waves in a solid is the basic concept of these methods. They can be

divided into the ultrasonic wave (or pulse) velocity method and the resonance frequency

method.

Ultrasonic wave velocity method

This is the most accurate measurement method for the elastic moduli [Wachtman, 1969].

A plane wave is propagated in a specimen. Two types of waves are of special interest. A

wave which vibration direction is equal to the propagation direction is called longitudinal,

whereas a transverse wave is characterized by a perpendicular vibration direction to the

propagation. Basically, the elastic moduli can be derived from the time a wave needs to

transit through the material. Therefore, several equations have been proposed [Bancroft,

1941; Hudson, 1943; Davies, 1948; Stanford, 1950; Tu et al., 1955]. However one has to

take into account the border conditions. An important influence on these equations

have the specimen dimensions. For sufficient high frequencies of the excitation wave the

specimen dimensions become infinite compared to the wavelength. In this case Young’s

modulus can be calculated by the following equation:

E = ρv2l(1 + ν)(1− 2ν)

1− ν(2.12)

where ρ represents the density (bulk density) of the material, v2l is the longitudinal wave

velocity and ν is the Poisson’s ratio. For the shear modulus a similar equation can be

applied using the transverse wave velocity:

G = ρv2t (2.13)

Poisson’s ratio can be derived from G and E.

The actual measurement is carried out by bonding a piezoelectric transducer to a spec-

imen and measuring the transit time of the excited sound waves. From this time one


Fig. 2.5.: Ultrasonic testing device with plugged sample, transducer and receiver are above and belowthe sample

can calculate the elastic moduli according to equations 2.12 and 2.13. In Figure 2.5

the setup for the longitudinal wave introduction is shown. The transducer is situated

above the sample whereas the receiver can be found below. As the method was devel-

oped throughout the world war two, the tremendous development of acoustical physics

during that time contributed to its broad application in the following years. This has

been summarized and discussed in the late 1950s by McSkimin [1959]. Its applicabil-

ity for high temperature measurement was also proven. Nowadays, ultrasonic velocity

measurements are used as a standard method for high temperature elastic moduli deter-

mination as well as for room temperature investigations [Auvray et al., 2001; Chotard

et al., 2008; Patapy et al., 2010]. For concrete it is used to asses the structure and

its properties (e.g. strength) [Jain et al., 2013]. Furthermore, Carreon et al. [2009]

found a correlation between the ultrasonic velocity and the hardness of the investigated

alumina-zirconia material, which showcase the versatile application possibilities of this

measurement method.

ASTM E494 - 10 and EN 12504-4:2004 are standards describing the actual measurement


0.00 0.01 0.02 0.03 0.04 0.05

−0.

50.

00.

51.

0

Time / s

Am

plitu

de /

mV

(a) Damped 440 Hz sound signal input

0 5000 10000 15000 20000

−15

0−

100

−50

0

Frequency / HzLe

vel /

dB

(b) FFT computed frequency spectrum

Fig. 2.6.: The signal converting way of the impulse excitation technique; a 440 Hz sound signal input istransformated into a frequency spectrum by a fast Fourier transformation (FFT) algorithm

setup and providing equations for the calculation of elastic constants.

Resonance frequency method

The resonance frequency method was firstly introduced by Forster [1937]. This method is

based on the fact that every material has its own resonance frequency. Pickett [1945a,b]

proposed equations for the computation of the elastic constants from the resonance fre-

quency for several specimen shapes. A first detailed description of the application of

this method and the computation of the elastic constants was given by Spinner and

Tefft [1961]. Nowadays ASTM E1875 - 08 and ASTM E1876 - 09 are standards describing

extensively the measurement setup and the calculation of elastic moduli for several spec-

imen shapes. A sample can either be excited constantly by a piezoelectric transducer

or by a mechanical impulse. The signal input is obtained by a piezoelectric receiver or

laser vibro meter; for the mechanical impulse method (also known as impulse excitation

technique) a microphone is used. The transducer method can be regarded as a frequency

scan. Once the resonance frequency of the specimen is introduced, the receiver signal

will increase immediately (resonance).

Only the impulse excitation technique (IET) was used in this study. Therefore, it will be

introduced more detailed here. IET provides an audio signal as output (shown in Figure


(a) Flexural mode (b) Torsinal mode

Fig. 2.7.: Schematic view of impulse excitation setup for a rectangular bar according to ASTM E1876

2.6). This signal is subsequently divided into single sine and cosine waves using the fast

Fourier transformation algorithm to obtain a frequency spectrum. Nowadays, this is

done automatically in most software assembled to the measurement devices. From the

spectrum of this input signal one can obtain the flexural or torsional frequency (ff or ft

respectively). There are specific vibration modes for bars, rods and discs corresponding

to the flexural and torsional frequency (see Figure 2.7 for a rectangular bar). As can be

seen in these figures the vibration is characterized by minimum and maximum amplitude

ranges. To avoid a suppression of the vibration it is important to mount the specimen

exactly in the minimum amplitude range, the so called nodes.

A further information to be gained from the impulse excitation measurement is the

damping. Every natural oscillation exhibits a decay. A materials vibration decay, the so

called damping, was attributed to the internal friction, defined as a materials capability

to disperse the vibration energy [Puskar, 2001]. It is calculated using the difference

of two subsequent amplitudes or a curve fit onto the decay signal. Especially for the

damping determination it has to be taken care of the mentioned exact sample adjustment

according to the vibration nodes.

The introduced elastic constants can be calculated in terms of impulse excitation tech-

nique according to Pickett [1945a,b] for a rectangular bar:

E = 0.9465mf2fb

l3

h3T1 (2.14)

where m, b, l and t are the mass, width, length and thickness of the bar respectively.


ff is the fundamental frequency in flexure and T1 is a correction factor to be found in

ASTM E1876. For the shear modulus the equation can be written:

G =4lmf2tbh

B

1 +A(2.15)

where ft is the fundamental frequency in torsion, A and B are correction factors which

can be calculated according to ASTM E1876. The calculation of damping is not described

in a standard. Forster [1937] first defined damping as the logarithmic decrement δ of

the vibration:

δ = lnznzn+1

(2.16)

Where zn and zn+1 are the n-th and n+ 1 amplitude of the damped vibration. Puskar

[2001] linked δ with the damping Q−1 to:

Q−1 =δ

π(2.17)

This equation can be found in most literature about damping nowadays. Due to the

development in computer technology it is common to fit an exponential function onto the

obtained damped frequencies. The estimates of this function are then used to determine

the damping, which is attracting more attention in the refractories research community

in recent years. An interesting analytic study related the thermodynamic definition of

damping to the actual measured damping and showed a relation between damping and

crack appearance [Panteliou et al., 2001]. More recent studies related the damping to

the thermal shock resistance of refractories. However, there is a great scattering in that

data especially for the damping, indicating problems with the sample adjustment and the

complicated nature of a thermal shock which can not be described by only one material

parameter [Pereira et al., 2011; Traon et al., 2011].

In conclusion the resonance method is an appropriate way of elastic moduli determina-

tion. Its setup is well documented and its analysis well understood. Therefore, it can

be found in many recent studies for high temperature and room temperature studies

on elastic moduli of refractories [Werner and Aneziris, 2012, 2013; Werner et al., 2013,

2014; Bohm et al., 2013; Quadling et al., 2013; Traon et al., 2013; Luz et al., 2013; Souza

et al., 2014]


2.2.3. Comparison of static and dynamic methods

From a theoretical point of view static and dynamic values should give the same results

since Young’s modulus is a constant (see section 2.1). The static modulus determination

can be regarded as isothermal due to the very slow stress introduction. The dynamic

method delivers adiabatic values, meaning that there is no heat compensation during

the measurement. However, there is a difference between adiabatic and isothermal mod-

uli. Landau and Lifshitz [1970] proposed a model to describe the relationship between

adiabatic (Ead constant entropy) and isothermal Young’s modulus (ET temperature con-

stant):

Ead = ET +E2Tβ

2T

9cp(2.18)

where β represents the volume expansion coefficient and cp the heat capacity per volume

unit at constant pressure. Considering this equation there is no reason for great discrep-

ancies of dynamic and static values at room temperatures. The difference between both

values at room temperature for alumina is as small as 0.02 % (data for the calculation

was taken from Munro [1997]). This is certainly smaller as the uncertainty from the

measurement itself. However, there were found remarkable differences of both values for

several materials, confusing engineers to choose a ”correct” value for calculations. This

subsection should give a brief overview of differences between both values for several

materials and some explanation for these discrepancies.

The comparison of statically and dynamically determined Young’s modulus is a topic

addressed very early by geophysicists. Ide [1936] firstly reviewed the difference between

both values in rocks. A significant variation in static Young’s modulus of rocks can

be attributed to differences in the stress applied for the load-deflection measurement.

Mostly due to cracks and cavities, which are closed by the applied load, leading to

higher yields of the material, the Young’s modulus values are scattered. This great

variance in statically determined values was the motivation to do a comparison with

dynamic values. He found differences of 5 to 40 % between statically and dynamically

determined Young’s moduli. In conclusion, he attributed the differences between static

and dynamic values to the discussed cavities and cracks in the material, which are been

closed due to the applied stress during the static measurement. This results in larger

deflection values which reduces Young’s modulus. Furthermore, Savich [1984] found a

relationship for static and dynamic E values of rocks of the form:

log(ESt) = a log(ED)− b (2.19)


a and b are dependent on the stress applied to the material. van Heerden [1987] approved

this relationship and suggested to expand it to large volume rock samples since static

measurements are of high costs.

For composite resin based materials dynamically determined E values where found to be

significantly larger than static values [Sabbagh et al., 2002]. This is particularly inter-

esting considering resin bonded alumina carbon material as the central study material.

While those composites investigated by Sabbagh et al. [2002] were only cured, carbon-

bonded materials rather provide a residual carbon structure than a polymer bond due to

the release of volatile products of the resin. Combining the results from the rock investi-

gations with those described above leads to the assumption of great discording between

static and dynamic elastic moduli for carbon-bonded alumina due to microcracks and

cavities mainly introduced during the release of volatile resin constituents.

Schulle et al. [2000] found a similar relation between statically and dynamically de-

termined Young’s modulus for refractory materials of different bonding type. They

investigated the Young’s modulus in a temperature range from 25 to 1500 ◦C. They did

not found a significant difference of ESt and ED at room temperature. However, the

difference at elevated temperatures was remarkable. Above 1000 ◦C the static modulus

decreased very strong whereas the dynamic modulus only slightly decreased. They at-

tributed this effect to an-elastic effects depending on the loading rate. They suggested

the use of dynamically obtained E values for thermal shock prediction and production

control due to the short time of stress application and release in the thermal shock pro-

cess. For the computation of thermal stresses arising in heating and cooling of linings

they suggested the use of static Young’s modulus values. This suggestion is satisfying

since during heating and cooling the stress rate is low compared to thermal shocks.

Furthermore, the model by Landau and Lifshitz [1970] confirms this suggestion.

In conclusion there are significant differences for statically and dynamically determined

Young’s modulus values for many materials. It was shown that these differences mainly

can be attributed to problems in static load-deflection tests, for example the closing of

cracks or cavities contributing to the deflection. Furthermore, the applied strain rate

contributes to the discrepancy between ESt and ED. These strain rates are very low

for static measurements, whereas they are very high for dynamic measurements. Just

this difference in the strain rates in combination with the highly heterogeneous system

”refractory” leads to big discrepancies between both values ESt and ED. Therefore, it is

advisable for engineering purpose to question the application and afterwards to choose

the appropriate measurement method. For example, in case of thermal shock prediction


dynamic values could be used since the apparent strain rate in this process might be more

comparable than for static values. However, the more accurate values can be obtained

by the dynamic measurement.

2.3. Thermal shock resistance assessement for refractories

Thermal shock resistance is one of the most investigated and important properties or

behavior of refractory products. There is a tremendous amount of literature describing

the resistance to thermal shock of refractories. Brochen [2011] gave a detailed review

of the estimation and experimental determination of thermal shock resistance parame-

ters. This subsection should give a brief overview of the recently used parameters and

experimental setups to assess and evaluate the thermal shock resistance of refractories.

As early as 1955 Kingery already addressed the problem of thermal shock resistance. He

gave a detailed review of factors influencing the rise of thermal stress in a material as

the Young’s or shear modulus (E,G), the thermal expansion (α), Poisson’s ratio (ν) and

the capability of the material or structure to conduct heat Kingery [1955] . Assuming

completely linear elastic behavior he proposed several so called R-factors, which basi-

cally provide the temperature gradient a material or structure will resist without failing.

Throughout the refractory community two of these factors are extensively used for the

quick assessment of thermal shock resistance of refractories. For a very rough thermal

shock (infinite heat transfer coefficient), the maximum temperature difference a material

can resist without failure is defined as

∆T = R =σ(1− ν)

Eα(2.20)

In the case of a constant heat transfer coefficient (mild thermal shock) Kingery intro-

duced the thermal conductivity λ to take the heat transfer into account:

R′ =σ(1− ν)λ

Eα(2.21)

Besides these two thermal shock parameters regarding the failure of the material, Kingery

proposed more factors for example for the calculation of a maximum heating or cooling

rate. However, the boarder conditions of these factors limit their application strictly to

”homogeneous isotropic bodies whose physical properties are substantially independent

of temperature” [Kingery, 1955]. This is far away from refractory products properties’.

2.3. Thermal shock resistance assessement for refractories 21

In addition to Kingery’s thermal shock resistance parameters describing the crack ini-

tiation, Hasselman [1969] considered not only the maximum stress a material can resist

but also the possibility of crack introduction and propagation in the material for his

so called thermal shock damage parameters considering the crack propagation. He

proposed the distinction between thermal shock fracture resistance and thermal shock

damage resistance. He introduced small Griffith flaws into his model. Thus, his approx-

imation is closer to real refractory products than Kingery’s. However, he also proposed

boarder conditions such as the temperature difference should not exceed the minimum

difference needed for thermal stress fracture. Otherwise additional thermal strains have

to be considered. Nevertheless, two of the thermal shock damage parameters proposed

by Hasselman are very popular in the refractory community [Hasselman, 1969, 1963].

R′′′′ =EGf

σ2(1− ν)(2.22)

where Gf represents the specific fracture energy. This parameter provides information

regarding the arresting and propagation of cracks related to thermal shocks. It can be

predicted whether the material failure might be catastrophic or cracks may be arrested.

A second thermal shock damage parameter proposed by Hasselman is the so called

”thermal stress crack stability” parameter:

Rst =

√Gfα2E0

(2.23)

where E0 presents the Young’s modulus of the material without cracks.

Comparing the concepts of Kingery and Hasselman it is obvious that there is a paradox

design situation. For maximization of R, R′ and Rst low values of E and α are of advan-

tage. Considering the crack propagation R′′′′ parameter it is obvious that high E values

will increase the probability of crack trapping. Besides this problem for the material

scientist there is a second drawback which is described by the temperature dependence

of the properties. They are assumed by Kingery and Hasselman as temperature indepen-

dent. However, as shown above for the Young’s modulus, they can not be considered as

independent. Therefore, high temperature values should be considered for the thermal

shock parameters proposed above. Thus, an intensive characterization of the Young’s

modulus of carbon-bonded alumina, as conducted in this study, should contribute to a

better understanding of thermal shock behavior of this material.

Brochen [2011] improved Hasselman’s and Kingery’s parameters by solving the heat


transfer problem numerically. He showed that his modified R parameters are more accu-

rate than the classical ones. However, a more accurate model of the wear mechanism is

nothing worth without adequate material parameter input. Still temperature dependent

values of the strength, Young’s modulus and thermal expansion need to be considered.

Salvini et al. [2012] furthermore adjusted Hasselman’s theory by introducing more recent

fracture mechanic concepts. They introduced the crack propagation energy γWOF (the

total work of fracture measured by the chevron notched beam test) and the crack initi-

ation energy γNBT (measured by the notched beam test). By doing so, they assumed to

consider the different crack interactions with the microstructure more accurate. They

could prove their equation to be more precise in forecasting the residual strength of a

material than Hasselman’s approach.

Besides these parameters, there are some experiments to asses and predict the thermal

shock behavior. There is the standard EN-993-11 for the prediction of thermal shock

behavior in Europe. The material (rectangular bars) is supposed to be heated up to

950 ◦C. After a holding time it should be cooled down to room temperature by an air

flow. To evaluate the thermal shock resistance two possible parameters are used. The

number of cycles a material could resist without failure at a load of 0.3 MPa is one

criteria. As a second the relative Young’s modulus or strength after five shock cycles

related to the unshocked values are used. A second method is the quenching in water

which is widely used in laboratory thermal shock assessment. However, besides a prob-

lem with the vaporization of the water during quenching, this procedure is not applicable

for hydrate-able materials. Furthermore, it could be problematic quenching a batch of

samples because the water is heated and therefore does not provide the same quenching

effect to all samples.

In the US the standard nowadays is ASTM C1171. It is comparable to the EN 993-11

since air is used to quench the material and the residual strength or Young’s modulus are

used for the thermal shock assessment. However, the temperature difference is supposed

to be 1200 ◦C.

There are more practical approaches which are nevertheless expensive and time consum-

ing like the Ribbon and Panel-Spalling tests [Tomsu and Ulbricht, 2009].

In conclusion it can be said, that the assessment of thermal shock behavior still is

a tough task to be solved by using temperature dependent material properties for the

computation of the thermal shock parameters in the specific temperature range needed.

2.4. Carbon-bonded alumina 23

2.4. Carbon-bonded alumina

Carbon-bonded alumina is the material investigated within this study. Therefore, the

following section will give a brief overview of its application in the refractory industry

and of its microstructure.

The range of application for this material is concentrated on so called functional refrac-

tories. Typical examples are slide gate plates, stoppers and sub-merged entry nozzles.

All of them are applied in continuous steel casting. Carbon-bonded alumina is used

due to its high reliability. An interruption of the casting process would involve many

problems. Besides the costs there could be for example health issues and frozen steel in

the tundish [Shultz et al., 1986].

There are two different applications for plates. In ladles the plate has to resist very

big temperature changes because they are cleaned by oxygen after the slag removal.

Therefore, a high thermal shock resistance is essential for these type of plates. On the

other hand plates in a tundish are not subjected such extreme temperature changes.

However, they have to resist high temperatures for a longer time and need therefore a

higher corrosion resistance [Itoh, 1998].

The second main application for carbon-bonded alumina are ladle shrouds and sub-

merged entry nozzles. The first one is used to transfer the molten steel from the ladle

to the tundish without oxidation and the entry nozzles are used for the transport of

the molten steel from the tundish to the water cooled mold. During service they will

be subjected enormous thermal shocks (sudden contact with molten steel). Therefore,

their thermal shock resistance has to be very high, otherwise the whole casting pro-

cess would have to be stopped [Itoh, 1998]. A serious problem of these materials is the

oxidation starting at 450 ◦C. The addition of so called anti oxidants (metallic powder)

presents a solution therefore and leads us to the microstructural characterization of these

materials.

2.4.1. Microstructure

Carbon-bonded alumina refractory materials are basically composed of three compo-

nents. The alumina as an oxide component, a carbon constituent and an organic binder

comprising the so called carbon bond. Other oxides can be added to the alumina in order

to modify the resulting properties (like zirconia for higher thermal shock resistance). As


Tab. 2.3.: Typical properties of glassy carbon derived from polymer precursors; Table taken from McKee[1973]

Bulk density 1.3− 1.5 g cm−3

Apparent porosity 0− 12 %Flexural strength 5− 80 MPaYoung’s modulus 14− 33 GPaThermal expansion coefficient 2− 3.5× 10−6 K−1

carbon constituents are used mainly natural graphite or carbon black. These components

should improve the thermal shock resistance by increasing the thermal conductivity of

the material, reducing the overall thermal expansion and introducing microcracks into

the material. The binder phase is basically also a carbon constituent [Itoh, 1998].

Nowadays, phenolic resins are state of the art binders for Al2O3-C products. Despite

their wide application in magnesia-carbon refractories, tar pitches are not the preferred

binders anymore, due to their noxious effects. Furthermore, the resin can be processed

(mixed) at room temperature in contrast to the pitch products. The resins transform

in two steps from a polymer compound into a residual carbon net or lattice. In a first

step the resin is cured at temperatures up to 200 ◦C. Depending on the kind of resin

(resol or novolac) a hardener, mostly in the form of hexamethylenetetramine, has to

be applied for the curing process. The second step is the actual transformation into a

carbonaceous product. The so called carbonization occurs mainly in the temperature

range of 200− 1000 ◦C and in inert gas atmosphere. In this temperature range volatile

products (H2O, CO, CO2, CH4 and H2) of the resin are released accompanied by a

densification of the material. Thereby, a density minimum occurs in the temperature

range of 200 − 550 ◦C. However, the resulting product can not be regarded as a pure

crystalline carbon like graphite [Fitzer et al., 1969; Gardziella and Suren, 1992].

Natural graphite in the form of flake graphite is the most common type of carbon filler

used for Al2O3-C products. It is relatively cheap and comprises a good thermal conduc-

tivity, low thermal expansion and chemical stability. Therefore it is added to Al2O3-C

products in amounts up to 30 wt % and more. However, natural flake graphite can be

regarded anisotropic as a single graphite crystal. Therefore, Al2O3-C products turn more

anisotropic by adding more graphite [Pierson, 1993a].

As mentioned above metal additives are more frequently used for the prevention of carbon

oxidation. Most commonly used are aluminum and silicon metal powders. During firing

they react with the carbon or atmospheric nitrogen to carbides and nitrides accompanied

2.4. Carbon-bonded alumina 25

with a volume expansion. Thus, by filling the voids of the microstructure the porosity

is reduced leading to a reduction of oxidation. Moreover, the metals react with the CO

and reduce it to C which contributes to the oxidation protection,too. A third effect is

the increase of strength of the material due to an increase in the bonding [Itoh, 1998].

Furthermore, in case of Si addition SiO(g) could be formed which can be transformed

into SiO2 by a further reduction of CO. Thus, a thin layer of SiO2 could be deposed on

the graphite and prevent its oxidation [Zhang, 2006].

Besides the addition of metals also carbides and boron containing oxides are used for

the oxidation prevention of carbon-bonded alumina [Yamaguchi, 2007].

More recently the addition of nanoscaled material to Al2O3-C refractories has been in-

vestigated. Roungos and Aneziris [2012] showed improvements of the thermal shock

resistance due to the addition of magnesium aluminate spinel, alumina sheets and car-

bon nanotubes. However, the alumina increased the overall strength which caused a

decrease of thermal shock resistance in terms of the earlier discussed parameters. Fur-

thermore, Roungos and Aneziris noted the importance of the mixing process regarding

the reproducibility.

Yet, most of these investigations have a strong application oriented focus. Therefore,

many process parameters are varied to obtain the best results for a certain applica-

tion. A systematic approach to understand the microstructural processes resulting in

a remarkable high thermal shock resistance has not been carried out yet. Therefore,

fundamental studies of the microstructure of carbon-bonded alumina could contribute

to a better understanding of the material and to a more accurate design of the refractory

products [Dupuy et al., 2013].

This study should be a contribution to such a fundamental understanding of the mi-

crostructure of pure alumina carbon materials. The Young’s modulus of elasticity is a

proper parameter to asses the microstructure of a material as described in this chap-

ter (see section 2.1). The relation of microstructure described by scanning electron

microscopy is a state of the art procedure. The indirect approach of microstructure

assessment using Young’s modulus of elasticity is used within this investigation, passing

the time consuming and only ex-situ applicable SEM investigations. Several composi-

tion parameters (e.g binder content, bonding system, graphite content) were changed

and the influence on the elasticity of the material at room and high temperature was

investigated. Furthermore, empirical models for the description of these influences will

be proposed. For a better understanding of these experiments, the following chapter


will give a detailed overview on the compositions investigated and the applied testing

methods.

27

3. Materials and methods

The purpose of this study was the investigation of elastic properties of carbon-bonded

alumina depending on its composition and the temperature. Therefore, three blocks of

experiments were carried out,

• Industry related compositions

• Reference compositions

• Filter coating bulk material and filter structures

These blocks are composed of experiments with different compositions and processing

parameters. The exact compositions and experimental procedures will be introduced in

the following sections.

3.1. Industry related compositions

Industry related compositions were used within the first experimental block. They were

derived from a mono-bloc stopper composition according to Roungos and Aneziris [2012]

and are shown in Table 3.1. They were chosen to obtain results for industry applications.

However, all additives were removed to start investigating a reference system. For this

block of experiments the variation of the bonding system (type of binder and amount

of binder) was chosen as composition factor influencing Young’s modulus. Furthermore,

the pyrolysis temperature and the molding pressure were chosen as technological factors.

Thus, this block consists of four independent experiments.

3.1.1. Variation of the binder content, bonding system and maximum

particle size

The raw materials used for this experiment were tabular alumina (T60/64, 99.5 % Al2O3,

Almatis GmbH, Ludwigshafen, Germany), natural graphite (AF, carbon content 96 -

28 3. Materials and methods

Tab. 3.1.: Industry related compositions

Raw material T20 T20-B10 T20-C T20-3wt %

Tabular Alumina

1.0 - 3.0 mm 0.0 0.0 0.0 35.60.5 - 1.0 mm 0.0 0.0 0.0 24.00.2 - 0.6 mm 43.0 39.4 43 0.00.0 - 0.5 mm 0.0 0.0 0 14.40.0 - 0.2 mm 32.0 29.6 32.0 0.0

Graphite d50=18µm 10.0 10.0 10.0 10.0Graphite d50=160µm 10.0 10.0 10.0 10.0Novolac resin liquid 2.0 2.0 0.0 2.0Novolac resin powder 4.0 8.0 0.0 4.0

Carbores® T10 liquid 0.0 0.0 2.0 0.0

Carbores® P powder 0.0 0.0 4.0 0.0Hexamethylene-tetramine1

10.0 10.0 10.0 10.0

1 related to the resin content

98 %, and NFL, carbon content 92 - 94 %, Graphite Kropfmuehl AG), liquid as well as

powder novolac resin, hexamethylenetetramine as hardener for the novolac resins (Mo-

mentive, Duisburg, Germany) and a liquid as well as modified coal tar pitch (Carbores®

P and Carbores® T10, Rutgers GmbH, Germany).

All samples were produced by mixing the components in a compulsory mixer (Maschi-

nenfabrik Gustav Eirich GmbH & Co. KG, Hardheim, Germany). In a second step,

bars (150×25×25 mm3) and cylinders (d = 50 mm, h = 50 mm) were uniaxially pressed

with a pressure of 100 MPa. Afterwards, the samples were cured up to 180 ◦C for the

resin and 300 ◦C for the Carbores® containing samples. Then they were fired at 1000 ◦C

in retorts filled with calcined pet coke (Mueco GmbH & Co. KG, Germany), having a

particle size between 0.2 and 2 mm, at a heating rate of 100 K/h with a dwell time of 5 h

at the maximum temperature.

In industry applications the binder content and type are varied widely in dependence

on the materials processing (e.g. uniaxial or isostatic pressing). Therefore, the binder

content was varied for the resin compositions from 6 to 10 wt %. The bonding system

was changed from resin to Carbores® at a fixed content of 6 wt %. Finally, the max-

imum particle size was altered from 0.6 to 3.0 mm by introducing a new composition.

However, the particle size distribution was not taken into account by the composition

design. The influence of these variations on the elastic properties were then investigated

at room temperature as well as up to 1450 ◦C.

3.1. Industry related compositions 29

Microphone

Sample

Sample support

Excitation device

Furnacechamber

Furnacelining

Fig. 3.1.: Schematic view of the IET-HT setup (Figure originally published in [Werner et al., 2013])

In preliminary experiments it was found that the particle size packing had a significant

influence on the retained bulk density and porosity of the material. Therefore, the re-

sults of the grain size dependence of Young’s modulus in this experiment were refused

and a more accurate experiment was carried out described in section 3.2.

Young’s modulus, shear modulus and Poisson’s ratio were obtained by the impulse ex-

citation technique (IET) according to ASTM-E1876.

The apparent porosity of the material was determined by the water immersion method

according to EN 993-1. Due to the absence of hydratable phases water was used.

For the high temperature measurement a furnace with an impulse excitation setup in-

side was used (HTVP1600, IMCE, Belgium) [Roebben et al., 1997]. Only the flexural

frequency was measured at elevated temperatures (schematic setting shown in Figure

3.1). Three samples of each composition were heated up to 1450 ◦C at a heating rate

of 5 K/min in an argon atmosphere with a dwell time of 2 h at maximum temperature

and flexural frequency was measured every 10 K. For heating as well as for cooling the

same conditions were applied. The mass loss of the material was carefully registered

(ex-situ) because a slight oxidation of the samples by residual oxygen within the furnace

was observed.

Furthermore, an additional oxidation measurement was carried out for the composition

T20 up to 1000 ◦C in air with a holding time of 60 min. A cycling experiment was ap-

plied to the same composition. Therefore, thermal cycles in steps of 200 K from 200 ◦C

to 1400 ◦C were applied to one sample. The last cycle up to 1400 ◦C was repeated. A

holding time of 60 min was applied at each maximum temperature. The heating rate

was the same as for the above described measurement.

For the evaluation of microstructural changes during the high temperature measurement


a Philips XL 30 (Philips, Germany) scanning electron microscope (SEM) was used by

comparing SEM pictures prior to and after the measurement.

X ray diffraction (XRD) analysis was carried out using a PHILIPS diffractometer with

Cu-κα radiation to obtain phase transitions due to the high temperature measurement.

The thermal expansion of the compositions was determined to be compared with the

results of the high temperature Young’s modulus. The measurements were carried out

using a Netzsch RUL/CIC 421 apparatus for determining refractoriness under load. A

pressure of 0.01 MPa was applied to the samples according to DIN-EN 993-19. The

same thermal cycle was applied as for the Young’s modulus of elasticity measurement.

However, the holding time was only 30 min. For this measurement only one sample per

composition was investigated. The thermal expansion of the filter bulk material was

obtained using a Netzsch DIL 402 C.

For the data analysis the software package ”R” was used [R Core Team, 2013].

3.1.2. Variation of the pyrolysis temperature

Due to the binder evolution during the pyrolysis of carbon-bonded alumina the influence

of different pyrolysis temperatures was studied.

The composition chosen for this experiment was T20-B10, a 0.6 mm and 10 wt % resin

composition (see Table 3.1). The forming and curing parameters were equal to those

explained above (subsection 3.1.1). Only, the maximum pyrolysis temperature was varied

in 3 steps (700 ◦C, 1000 ◦C and 1400 ◦C).

The one cycle high temperature measurement of Young’s modulus up to 1450 ◦C as well

as the thermal expansion measurement were carried out according to the description in

subsection 3.1.1.

3.1.3. Variation of the molding pressure for porosity variation

As shown in the fundamentals chapter the Young’s modulus is dependent on the poros-

ity. Since also the corrosion resistance of carbon-bonded alumina is determined by the

porosity, the investigation of the porosity influence on E is essential. Thus, the influence

of porosity on the Young’s modulus was studied in this experiment. Therefore, T20-3 a

3.0 mm and 6 wt % resin composition was chosen (see Table 3.1). Apart from the mold-

ing pressure the sample preparation was completely the same as for the experiment in

subsection 3.1.1.

3.2. Reference compositions 31

The molding pressure was varied in 5 steps (20, 40, 70, 100 and 130 MPa) to obtain

different porosity levels. Preliminary experiments revealed the molding pressure as the

factor with the largest influence on porosity and Young’s modulus [Werner et al., 2014].

The one cycle high temperature measurement of Young’s modulus up to 1450 ◦C was

carried out according to the described procedure in subsection 3.1.1.

The elastic properties at the pressure levels were compared by using the Tukey range

test with a p-value of 0.05 (also known as Tukey’s HSD [honest significant difference]

test). This is a single step multiple comparison test.

The high temperature experiments were interpreted with repeated measures ANOVA

between-subjects in the temperature range from 25 ◦C to 1025 ◦C (former pyrolysis tem-

perature). Thereby the temperature was defined as the within-subjects and the porosity

level as the between-subjects factor [Scheiner and Gurevitch, 1993]. Furthermore the

Young’s moduli at the different porosity levels were compared by a pairwise t-test with

a p-value of 0.05, which was adjusted according to the Bonferroni-Holm method [Holm,

1979; Werner et al., 2014].

3.2. Reference compositions

The results of the industry related compositions revealed an influence of the maximum

alumina particle size on the Young’s modulus. However, a possible influence of the parti-

cle size distribution of the compositions on the elastic properties could not be eliminated

and furthermore the difference between the maximum alumina particle sizes seemed to

be too small. Furthermore, the influence of the carbon containing phase has not been

studied in the experiment above.

Therefore three factors influencing the microstructure of carbon-bonded alumina were

chosen. The graphite content was varied in four steps (0, 10, 20 and 30 wt %). The

maximum particle size was altered in three steps (0.045, 1 and 3 mm). Finally, at a

carbon filler content of 10 wt % the type of filler was varied (carbon black, fine graphite

(AF), a mixture of fine and coarse graphite and coarse graphite (NFL)). It was used the

following carbon black powder as raw material (Luvomaxx N-991, Lehmann & Voss &

Co. KG, Germany, 99.0 wt % carbon, ≥0.01 wt % ash content, primary particle size of

200 - 500 nm). The particle size distribution for the 1 and 3 mm composition was set to

n=0.65. Preliminary experiments showed the highest bulk density for this coefficient.

The compositions for the different graphite contents are shown in Table 3.2. For the


carbon filler variation the particle size distribution of the 10 wt % graphite content com-

position was arbitrarily chosen and only the carbon filler was varied (see Table 3.2).

The elastic properties (Young’s modulus, shear modulus and Poisson’s ratio), apparent

porosity and bulk density were investigated at room temperature. Furthermore, the

Young’s modulus was measured from room temperature up to 1450 ◦C for all composi-

tions. The thermal expansion was also investigated.

3.3. Carbon-bonded open cell foam structures

Thermal shock resistance is the most essential property of these filter structures. Pro-

viding the elastic properties for these structures could reduce experimental affords to a

minimum and therefore could reduce research and development costs, too.

Therefore in this section the coating slurry of a metal melt filter was investigated regard-

ing its elastic properties at room and high temperature to provide information regarding

the strut material. Afterwards the actual filter structure was investigated under the

same conditions. The composition of the filter coating slurry was prepared according

to Emmel and Aneziris [2012]. The results will be discussed regarding a relationship

between the elastic properties of the bulk material and the filter structures according to

Gibson and Ashby [1997].

3.3.1. Filter coating bulk material

Within this experiment the influence of the binder content and the porosity on the elastic

properties were investigated. Therefore, two different compositions were used (shown in

Table 3.3 and 3.4).

Additional raw materials, except those already introduced above (subsection 3.1.1 and

section 3.2), were tabular alumina (Martoxid MR70, 99.8 % Al2O3 Martinswerk GmbH,

Germany), a dispersing agent (Castament VP 95 L, BASF AG, Ludwigshafen, Germany),

an anti foam agent (Contraspum K 1012, Zschimmer & Schwarz Mohsdorf GmbH &

Co. KG, Germany), a ligninsulfonate (T11B, Otto-Dille®, Baeck GmbH and Co. KG,

Germany) as temporary binder and a polymethyl methacrylate (Porlat K85, Zschimmer

& Schwarz Mohsdorf GmbH & Co. KG, Germany) as a pore forming agent.

The bulk material was prepared as follows. Prior to shaping, a slurry was obtained by

homogenizing in a ball mill for 24 h. For the pressed samples the slurry had to be dried

prior to pressing at 110 ◦C. Bars of 70 × 7 × 7 mm3 were slip casted as well as pressed

3.3. Carbon-bonded open cell foam structures 33

Ta

b.

3.2

.:R

efer

ence

com

posi

tions;

the

com

posi

tion

nam

eca

nb

ere

ad

as

follow

s:T(abu

laraluminaofthemaximum

particle

size)-Y

-(mm

andof

agraphitecontentof)X(w

t%)

Raw

mate

rial

T-0

.045-X

T-1

-XT

-3-X

dm

ax

=0.0

45

mm

dm

ax

=1.0

mm

dm

ax

=3.0

mm

wt%

Gra

phit

eA

F/N

FL

0.0

10.0

20.0

30.0

0.0

10.0

20.0

30.0

0.0

10.0

20.0

30.0

Tabula

rA

lum

ina

0-

0.0

45

100.0

90.0

80.0

70.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0-

0.2

mm

0.0

0.0

0.0

0.0

9.8

3.5

0.0

0.0

15.7

7.0

0.0

0.0

0-

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mm

0.0

0.0

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0.0

49.7

44.8

36.9

25.3

22.4

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0.0

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40.5

41.7

43.1

44.7

13.2

12.9

12.6

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0.0

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0.0

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0.0

0.0

0.0

9.9

8.3

8.6

12.9

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0.0

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0.0

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38.8

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liquid

2.0

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2.0

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cre

sin1

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der

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etra

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Tab. 3.3.: Filter coating bulk material composition according to Emmel and Aneziris [2012]; Threedifferent levels of porosity were obtained by introducing a pore forming agent

Raw material AC4wt %

Alumina Martoxid MR 70 d50=0.5-0.8µm 64.8

Carbores® P powder 19.6Carbon black d50=200-500 nm 6.2Graphite d50=18µm 7.6Castament VP 95 L 0.3Contraspum K 1012 0.1Ligninsulfonate T11B 1.5Porlat K851,2 0-150µm 0.0Water content1 75.01 related to the solid content2 was varied in 3 steps of 20 wt % each (20, 40, 60)

Tab. 3.4.: Filter coating bulk material composition with Carbores® P variation to study its influenceon the elastic properties

Raw material AC5 AC10 AC20 AC30wt %

Alumina Martoxid MR 70 d50=0.5-0.8µm 95.0 90.0 80.0 70.0

Carbores® P powder 5.0 10.0 20.0 30.0Castament VP 95 L 0.3 0.3 0.3 0.3Contraspum K 1012 0.1 0.1 0.1 0.1Ligninsulfonate T11B 1.5 1.5 1.5 1.5Water content1 81 79 75 71.01 related to the solid content

at 150 MPa to obtain different porosity levels. A pore forming agent was introduced for

obtaining higher porosity levels. Its amount was varied in three steps of 20 wt % each,

from 20 to 60 wt %. The samples containing pore forming agent were only pressed.

Afterwards, the samples were heat treated at 800 ◦C for 3 h in a pet coke filled retort

according to Emmel and Aneziris [2012].

For the high temperature measurement of Young’s modulus three samples of AC4 were

heated up to 1000 ◦C and 1450 ◦C at a heating rate of 5 K/min in an argon atmosphere

with a dwell time of 2 h at maximum temperature and flexural frequency was measured

every 10 K. For heating as well as for cooling the same conditions were applied. The

mass loss of the material was carefully registered (ex-situ) because a slight oxidation of

the samples by residual oxygen within the furnace was observed.

3.3. Carbon-bonded open cell foam structures 35

In a second experiment the carbon fillers (graphite and carbon black) were removed to

retain only alumina and Carbores® P, to study the influence of the binder phase on

the elastic properties of the composite. Therefore, the Carbores® P content was varied

from 5 to 30 wt % (see Table 3.4). All samples were mixed and pressed according to the

above introduced procedure. The heat treatment was also the same.

3.3.2. Filter structures

Metal melt filters for steel melt filtration were prepared according to Schwartzwalder

[1963]. The slurry was prepared exactly according to Emmel and Aneziris [2012] in

a two step process. At first an impregnation slurry was produced by dry mixing and

adding subsequently deionized water. This slurry was then used to impregnate PU-foams

(150×50×25 mm3). Afterwards, the foams were dried for 12 h at 25 to 40 ◦C. The second

step was the addition of a second layer of the same material by spraying.

The heat treatment as well as the high temperature measurement up to 1000 ◦C of E

was the same as for the bulk material.

37

4. Results and discussion

Within this chapter the results of the three previously introduced experimental blocks

will be presented and discussed. In addition, at the end of each section a concluding

discussion subsection can be found.

4.1. Industry related compositions - Processing and

composition influence on Young’s modulus

In this section the influence of changing either the composition or the processing of the

material was investigated. Therefore, a reference composition was chosen (T20, 0.6 mm

alumina particle with 20 wt % graphite content, 6 wt % resin) and firstly analyzed. Af-

terwards the binder content, type of binder and the pyrolysis temperature were varied.

Furthermore, the influence of oxidation and cycling during a high temperature mea-

surement was studied for the reference composition. The last experiment of this block

investigated the influence of the porosity on the Young’s modulus at room and high

temperature.

4.1.1. Composition T20 an exemplary carbon-bonded alumina

Composition T20 was chosen as reference system to which all samples will be compared

within this section. The reason for this decision was the graphite content which is

in accordance to the used graphite amount in submerged entry nozzles and stopper

systems.

The room temperature values of Young’s modulus and porosity are shown in Table 4.1.

The high temperature investigation of the reference material is shown in Figure 4.1a. For

a better comparability, the Young’s modulus at elevated temperatures was normalized

to the room temperature value. A measurement in argon atmosphere was carried out

up to 1450 ◦C. A second measurement in air was done up to 1000 ◦C. Furthermore, the

38 4. Results and discussion

0 500 1000 1500

−10

0−

500

5010

015

0

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

ArgonAir

(a) Air and Argon atmosphere

200 400 600 800 1000

7075

8085

9095

100

Temperature / °C

mm

0 / %

(b) Mass change

Fig. 4.1.: Young’s modulus of elasticity variation versus temperature normalized to room temperaturevalue E0 for T20 and the oxidation experiment; on the right the mass change during the oxidation cycleis shown

mass change during the oxidation experiment was triggered and can be seen in Figure

4.1b.

For the argon measurement there was a clear hysteresis between heating and cooling,

which resulted in lower E values compared to the initial ones. The evolution of Young’s

modulus of elasticity for the reference composition T20 could be classified into three

significant stages. Stage 1: 25− 400 ◦C

In this range E decreased almost linearly as for the pure alumina.

Stage 2: 400− 1200 ◦C

E increased significantly within this temperature range. Approximately 100 − 200 ◦C

above the former pyrolysis temperature the peak of the curve was reached.

Stage 3: 1200− 1450 ◦C

Above the former pyrolysis temperature, in the third stage, there was a slight decrease of

E compared to the maximum value at about 1200 ◦C. At the holding time an increase of

E was observed, which was found to be time dependent (see Figure 4.3). First sintering

stages could contribute to this increase.

The cooling behavior might also be divided into these stages but vice versa. However, the

temperature ranges were slightly switched. In stage 3 after the soak time E remained

almost constant. The decrease of E in stage two (similar to the remarkable increase

4.1. Industry related compositions - Processing and composition influence on Young’s modulus 39

Tab. 4.1.: Apparent porosity πa and E of the investigated compositions at room temperature; meanvalues and the confidence interval for α = 0.05 are shown

Composition πa / % E/ GPA

T20 18.16± 0.21 7.94± 0.25T20-B10 23.00± 0.39 8.83± 0.26T20-C 16.69± 0.33 7.36± 0.16

during heating), occurred at 1150 ◦C. This decrease was significantly steeper than the

increase during heating. The transition from stage 2 to stage 1 was very smooth and to

be found around 900 ◦C. E decreased slightly down to room temperature. The residual

Young’s modulus was significantly lower than the initial value.

The results of the oxidation experiment are shown in Figure 4.1b. Up to 400 ◦C the

evolution of E for the cycle in air was the same as in argon atmosphere. Above this

temperature the difference was very obvious. From 400− 650 ◦C there was a remarkable

decrease of E in air, while in argon E increased strongly. In the temperature range

of 650 − 1000 ◦C E increased in air, disproving the assumption of a constant decrease

due to a continuing oxidation. The ongoing oxidation was proven by the constant mass

loss (see Figure 4.1b). Thus, it was assumed that microstructural changes (e.g. gap

closure between grains and matrix) compensated this oxygen attack up to 1000 ◦C. At

the holding time there was a strong decrease of E observed, which continued at cooling

due to an ongoing oxygen attack. After one measurement cycle the Young’s modulus

was reduced below 80 % of its initial value which basically resulted in the destruction of

the material.

The pyrolysis temperature seemed to determined the temperature at which the maximum

value for E was reached. For further investigation a thermal cycling experiment was

carried out in steps of 200 K from 200 ◦C to 1400 ◦C. Figure 4.2b presents an overview of

E loss and peak values for the cycles. After each cycle E was decreased. The maximum

values of E for each cycle indicated the same behavior like for one continuous cycle up

to 1450 ◦C (see Figure 4.1a). The highest peak was found at 1000 ◦C. All the cycles

showed the three characteristic stages, defined above (see Figure 4.2a). However, the

beginning of the increase and also of the decrease in stage two changed as a function

of the maximum temperature of the cycle. There was a lowering of Young’s modulus

of elasticity after each cycle. The earlier mentioned oxygen attack certainly contributed

to the increase of the porosity, resulting in lower E values. At the end of the whole

cycling experiment the apparent porosity reached a value of 24 % which is an increase of

approximately 6 %.


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

200 °C400 °C

600 °C

800 °C

1000 °C 1200 °C

1400 °C Zyklus 1

1400 °C Zyklus 2

(a)

Maximum cycle temperature / °C

(E0

−E

i)E

i / %

200 600 1000 1400

−60

−50

−40

−30

−20

−10

0

050

100

150

(ET

max

−E

i)E

i / %

E0 − Ei EiETmax − Ei Ei

(b)

Fig. 4.2.: Young’s modulus of elasticity evolution within the cycling experiment for T20; Ei is the initialE value before the experiment started, E0 presents the E value at room temperature after each cyclewhile ETmax is the maximum E value after the holding time

0 20 40 60 80 100 120

05

1015

20

Temperature / °C

(E−

Ei)

Ei /

%

0 20 40 60 80 100 120

ResinCarbores

(a) Change in type of binder

0 20 40 60 80 100 120

05

1015

20

Temperature / °C

(E−

Ei)

Ei /

%

0 20 40 60 80 100 120

6 wt%10 wt%

(b) Change in amount of resin

Fig. 4.3.: Change of Young’s modulus during the soak time of the resin (T20 and T20-B10) andCarbores® bonded (T20-C) materials, Ei represents the initial value of E at 1450 ◦C


4.1.2. Influence of different binder systems

In Table 4.1 the Young’s modulus and porosity of the reference composition (T20) at

room temperature can be found. The apparent porosity of approximately 18 % was

in good agreement with other studies of this material [Roungos and Aneziris, 2012].

The Young’s modulus was as low as assumed due to the graphite and resin addition to

the alumina. Obviously, the minor phase or phases (graphite and resin) determine the

macroscopic elastic behavior of the material.

The increase of the resin content (6 ⇒ 10 wt %, T20-B10) resulted in a higher E value

and porosity at room temperature. This seems paradox since the Young’s modulus is

reduced by increasing porosity. However, the increase of resin resulted in a stronger

release of volatile products during pyrolysis which increased the porosity. On the other

hand there was more residual carbon left, compared to the lower resin content material,

contributing to an increase in the stiffness of the material.

The change from resin to Carbores® (T20-C) as a binder resulted in a decrease of

porosity but also in a slight decrease of E at room temperature. However, T20 and

T20-C can be regarded as approximately equal stiff. The reduction in porosity of T20-C

can be explained with the melting of Carbores® at around 300 ◦C resulting in a closing

of voids and cavities remained from the pressing.

The influence of different amounts of resin on the Young’s modulus evolution at high

temperatures is shown in Figure 4.4a. The maximum increase of E at heating increased

with decreasing resin content. Also the increase of E during the holding time was

stronger, the less resin there was within a composition (see Figure 4.3b). This was

clearly due to the resin, which inhibited the alumina grains from sintering since it could

be found between them. For the 10 wt % resin composition the decrease of E after

one cycle was slightly higher (−50 %) than for the 6 wt % composition (−35 %). This

might also be related to a lower sintering during holding time, due to the higher binder

amount which inhibited the sintering of the alumina grains. Furthermore, the decrease

during cooling started at a higher temperature (1300 ◦C) for the higher resin containing

composition.

Comparing the dilatometer measurements in Figure 4.4b reveals a hysteresis behavior

for both compositions (T20 as well as T20-B10). The expansion during heating was

almost linear up to 1000 ◦C. However, the slope of the expansion was significantly lower

for the 10 wt % composition. The expansion during heating was linear for T20-B10 up to


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

6 wt%10 wt%

(a) Young’s modulus measurement

0 500 1000 1500

0.0

0.5

1.0

1.5

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

6 wt%10 wt%

(b) Dilatometer measurement

Fig. 4.4.: Young’s modulus of elasticity variation versus temperature normalized to room temperaturevalue E0 for 6 and 10 wt % resin bonded material; on the right the thermal expansion is shown

1450 ◦C whereas for T20 a steeper increase above 1000 ◦C was observed. During holding

time a small shrinkage could be observed for T20 whereas there was almost no shrinkage

for T20-B10. The decrease of expansion during cooling was somehow linear for both

materials, however the overall expansion after one cycle was higher for T20 than for

T20-B10.

The comparison between the resin and Carbores® bond is presented in Figure 4.5. The

Young’s modulus evolution of both compositions was almost similar as can be seen in

Figure 4.5a. The maximum increase at heating was about 10 % higher for the Carbores®

containing composition. Mainly there were two significant differences in the curve charts

observed. Above 1150 ◦C there was a decrease of E for the resin containing composi-

tion which was less for the Carbores® containing composition. Furthermore, the strong

decrease of E at cooling was more rapid than for the resin composition. The overall

lowering of E after one cycle was found to be almost equal between 35 and 40 % for both

compositions. Also, the behavior during soak time was the same (see Figure 4.3a).

Clearly the Carbores® bond provided a lower overall expansion than the resin as can

be seen in Figure 4.5b. Qualitatively, there was almost no difference for both compo-

sitions. The expansion at heating was followed by a small shrinkage during holding.

The contraction during cooling was linear till 1100 ◦C, and below it tended to get lower

resulting in a residual expansion of the material. This hysteresis within the contraction


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

ResinCarbores P


0 500 1000 1500

0.0

0.5

1.0

1.5

Temperature / °C(l

−l 0)

l 0 /

%

0 500 1000 1500

ResinCarbores


Fig. 4.5.: Young’s modulus of elasticity variation versus temperature normalized to room temperaturevalue E0 for resin and Carbores® bonded materials; on the right the thermal expansion is shown

Tab. 4.2.: Mass loss, change of apparent porosity (difference of initial and end value; πia − πe

a) apparentporosity and Young’s modulus at room temperature after the measurement cycles

Composition (m-m0)/m0 / % πia − πea πa / % E / GPA

T20 -1.58± 0.34 4.00± 0.52 22.16± 0.31 5.45± 0.40T20-B10 -2.38± 0.21 2.47± 0.68 25.47± 0.29 4.72± 0.11T20-C -1.94± 0.22 4.54± 1.03 21.23± 0.71 4.09± 0.40

path can be found also in the Young’s modulus of elasticity curves. The differences in

the overall expansion might be attributed to the differences in the carbonization process

of the binders.

In Table 4.2 the change in porosity, sample mass and Young’s modulus after one cycle

are shown. Although an argon atmosphere was applied during the measurement, a mass

loss could still be observed. This could be attributed either to residual oxygen left in

the furnace lining, or to the release of volatile parts of the resin which have not been

released during the pyrolysis. The mass loss was to be found lowest for the reference

composition T20 followed by the Carbores® composition and the 10 wt % resin T20-B10.

This composition had the highest initial porosity which could contribute to a stronger

oxidation due to a bigger surface to be attacked. However, the increase in porosity did

not correlate to the mass loss.


Tab. 4.3.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) for the binder influence on the high temperature measurement of E up to 1450 ◦C;for each pair a p-value is shown, p < 0.05 indicates a significant difference

T20 T20-B10

T20-B10 5.7e− 11 −T20-C 7.2e− 14 8.9e− 15

Despite the qualitative observation of the influence of binder type and content, an

ANOVA and a pairewise t-test for the different binder levels at each temperature was

carried out. The ANOVA confirmed the obvious influence of the binder content and

type as well as of the temperature on the Young’s modulus (p < 0.05). The results of

the t-test can be seen in Table 4.3. For all pairs of binder amount or type there was a

significant difference during the high temperature measurement. However, this quanti-

tative evaluation has to be combined with the visual observation of the results, as done

above.

These results revealed a significant influence of the binder on the Young’s modulus up

to 1450 ◦C. Furthermore, it was shown that the oxidation of the material accompanied

by a decrease of E was kind of superimposed by microstructural processes not described

yet. Therefore, the influence of the pyrolysis temperature on the Young’s modulus up

to 1450 ◦C was investigated.

4.1.3. Influence of different pyrolysis temperatures

The composition was treated with three different pyrolysis temperatures of 700 ◦C,

1000 ◦C and 1400 ◦C. According to the previous results, the highest Young’s modulus

during heating was always observed around the former pyrolysis temperature. Therefore,

this experiment was designed to confirm or deny this observation and to understand the

microstructural changes during reheating of the material.

In Figure 4.6 the basic properties (E, G, ν, πa and ρb) at room temperature are shown.

Moreover, in Table 4.4 the results of a multiple comparison of means test to obtain

significant differences between the different pyrolysis temperatures are presented. The

apparent porosity and bulk density were determined on three samples, whereas for the

other measurements 10 samples were investigated. There was an increase of apparent

porosity with increasing pyrolysis temperature observed. Correspondingly, the bulk den-

sity was found to be decreased. However, there was no significant influence of pyrolysis

temperature above 1000 ◦C on the apparent porosity (see Table 4.4). The Young’s and


Pyrolysis temperature / °C

Bul

k D

ensi

ty /

g cm

−3

700 1000 1400

2.50

2.55

2.60

2.65

2.70

1516

1718

1920

App

aren

t por

osity

/ %

Bulk densityApparent porosity

(a)

Pyrolysis temperature / °CYo

ung'

s/S

hear

mod

ulus

/ G

Pa

700 1000 1400

05

1015

20 Young's modulusShear modulus

(b)

Pyrolysis temperature / °C

Poi

sson

's r

atio

700 1000 1400

0.06

0.08

0.10

0.12

0.14

−1.

2−

1.1

−1.

0−

0.9

−0.

8−

0.7

−0.

6

(l−

l 0)

l 0 /

%

Poisson's ratio(l − l0) l0

(c)

Fig. 4.6.: Elastic and physical properties of the T20-B10 samples treated at pyrolysis temperatures of700 ◦C, 1000 ◦C and 1400 ◦C; measured at room temperature

Tab. 4.4.: Results of the Tukey range test with a p-value of 0.05 for the different pyrolysis temperaturesand response values (E, G, ν, πa and ρb); the values tested were evaluated at room temperature, p < 0.05indicates significant differences between the tested pair

Temperature pair pE pG pν pπa pρb p(l−l0)/l01000 ◦C− 700 ◦C < 0.005 < 0.005 0.073 < 0.005 < 0.005 < 0.0051400 ◦C− 700 ◦C < 0.005 < 0.005 0.008 < 0.005 < 0.005 < 0.0051400 ◦C− 1000 ◦C < 0.005 < 0.005 0.594 0.084 < 0.005 0.983

shear modulus were significantly decreased due to the increase in pyrolysis temperature.

There was no significant influence of the pyrolysis temperature on Poisson’s ratio. Fur-

thermore, the length change of the samples was found to be increased up to 1000 ◦C.

However, from 1000 ◦C to 1400 ◦C there was no significant change in ∆l. These results

confirm those found by Franklin and Tucker [1995] and Yamaguchi [2007] for carbon-

bonded magnesia materials.

In Figure 4.7 the Young’s modulus in dependence on the temperature, the thermal ex-

pansion and the soak time behavior during Young’s modulus measurement are shown.

The maximum value of E was found at the former pyrolysis temperature. Further-

more, the residual Young’s modulus after one cycle was found to be almost equal for

all treatments at around 5 GPa. A second interesting observation was the reduction of

the hysteresis behavior with an increasing pyrolysis temperature. Moreover, in Figure

4.7b it can be seen that there were no differences regarding the increase of E during the

soak time. Above the former pyrolysis temperature a slight decrease of E was observed,

confirming the previous results.

The expansion measurement revealed a significant correlation between the pyrolysis tem-


0 500 1000 1500

05

1015

2025

Temperature / °C

E /

GP

a

0 500 1000 1500

700 °C1000 °C1400 °C


0 20 40 60 80 100 120

02

46

8

Time / min(E

−E

i)E

i / %

700 °C1000 °C1400 °C

(b) Soak time behavior

0 500 1000 1500

−0.

20.

00.

20.

40.

60.

81.

0

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

700 °C1000 °C1400 °C

(c) Dilatometer measurement

0 500 1000 1500

0e+

004e

−06

8e−

06

Temperature / °C

α / K

−1

0 500 1000 1500

700 °C1000 °C1400 °C

(d) α(T )

Fig. 4.7.: Young’s modulus and thermal expansion measurements up to 1450 ◦C for the compositionT20-B10 at different pyrolysis temperatures


●

●

●

●

●

20 40 60 80 100 120

2.40

2.45

2.50

2.55

2.60

2.65

2.70

2.75

Molding pressure / MPa

Bul

k D

ensi

ty /

g cm

−3

1214

1618

2022

App

aren

t por

osity

/ %

● Bulk densityApparent porosity

(a) Apparent porosity and bulk density versusmolding pressure

●

●

●

●

●

20 40 60 80 100 120

23

45

67

89

Molding pressure / MPaYo

ung'

s an

d sh

ear

mod

ulus

/ G

Pa

● Young's modulusShear modulus

(b) E and G versus molding pressure

Fig. 4.8.: Effect of molding pressure on the apparent porosity, bulk density, Young’s modulus and shearmodulus at room temperature

perature and the thermal expansion (linear CTE). The higher the pyrolysis temperature

was, the lower was the overall thermal expansion and therefore the expansion coefficient.

In Figure 4.7d the coefficient of thermal expansion α is shown in dependence on the

temperature. The 700 ◦C composition showed an increasing α up to its pyrolysis tem-

perature. Above it remained constant and decreased significantly at around 1250 ◦C.

The higher the former pyrolysis temperature was the later (at higher temperatures) an

increase of α was registered. This correlation is similar to the observed behavior for the

Young’s modulus measurement. It seems that the macroscopic expansion behavior was

somehow linked to the elasticity of the carbon-bonded alumina.

4.1.4. Influence of porosity

For the porosity experiment composition T20-3 was used. To change the porosity of the

samples the molding pressure was changed within 5 steps (20, 40, 70, 100 and 130 MPa).

As anticipated, there was a remarkable effect of this modification on the apparent poros-

ity and bulk density at room temperature as shown in Figure 4.8a. The higher the mold-

ing pressure was, the lower was the apparent porosity and correspondingly the higher

was the bulk density of the samples. Furthermore, there was a significant increase of

the Young’s modulus and shear modulus due to the increasing molding pressure as can


●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●●

●●

●

●

●

●

●

0.14 0.16 0.18 0.20 0.22

56

78

9

Pore volume fraction

E /

GP

a

E = E0e−bP

E = E0(1 − P)m

linear reg

Fig. 4.9.: Young’s modulus E plotted versus pore volume fraction P including the linear regression model(solid line), the Spriggs approach Spriggs [1961] (dotted line) and the Phani model [Phani and Niyogi,1986] (dashed line) fitted to the data

be seen in Figure 4.8b. Nevertheless, the influence of the molding pressure was decreas-

ing with higher pressures, due to a very high rate of densification at lower pressures,

decreasing rapidly at higher pressures [Reed, 1995].

All pairs of molding pressure were tested by applying the Tukey range test (multiple

comparison of means, single step method) and significance for almost all of them was

detected. Nevertheless, there was no significant effect increasing the molding pressure

from 100 to 130 MPa (p > 0.10). Furthermore, the significance of the effect of increasing

molding pressure from 40 to 70 MPa was hardly significant (0.05 < p < 0.10). Despite

significant effects on the apparent porosity and bulk density, there was no significant

effect on Young’s modulus and shear modulus observed by increasing the molding pres-

sure from 70 to 100 MPa (p > 0.10). This could be due to the strong standard deviation

of the Young’s modulus and shear modulus values of the 70 MPa batch as indicated in

Figures 4.8a and 4.8b. A contribution to this deviation could be the oxygen partial pres-

sure inside the pet coke filled retort, which can be considered as a function of the sample

position during coking. Thus, differences in oxidation of the samples could contribute

to a deviation in the microstructure of the sample and could affect the Young’s modulus

and shear modulus.

In Figure 4.9 and Table 4.6 the experimental values of Young’s modulus were plotted

against the pore volume fraction, followed by fitting them to a linear regression model and


−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

Porosity / %

13.9914.3316.3117.8421.72

(a) Normalized Young’s modulus variation

0 500 1000 1500

05

1015

2025

Temperature / °CE

/ G

Pa

0 500 1000 1500

Porosity / %

13.9914.3316.3117.8421.72

(b) Young’s modulus variation

Fig. 4.10.: Young’s modulus variation versus temperature and normalized to room temperature valueE0 for the tested porosity levels

to two well known and widely used models from the literature [Spriggs, 1961; Phani and

Niyogi, 1986]. With increasing porosity the Young’s modulus was significantly decreased.

Within the observed porosity range this correlation can be described as linear according

to the observed adjusted-R2 values.

The results of the high temperature measurement of Young’s modulus (E) can be re-

garded qualitatively similar for all porosity levels (Figure 4.10a) considering the normal-

ized values (∆E/E0). There was a major increase for E between 400 and 1000 ◦C. Above

this temperature a slight decrease in E was observed. After the holding time a steep

decrease of E down to 1200 ◦C was detected. From 1200 ◦C down to room temperature E

was slightly decreasing. This behavior was similar to that observed for the compositions

tested above and comprised the same three stages. Besides this somewhat similar behav-

ior, there were quantitative differences between the high temperature Young’s modulus

values at different porosity levels. As shown in the previous results, Young’s modulus

decreased due to the porosity increase at room temperature. Hence, for higher porosity

the high temperature values of Young’s modulus were correspondingly lower (see Figure

4.10b).

A statistical analysis was carried out for the normalized Young’s modulus (E −E0/E0)

results for temperatures up to 1025 ◦C (shown in Table 4.5). The temperature limit was

chosen due to assumed microstructure changes above this temperature (former pyrolysis


Tab. 4.5.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) for the porosity influence on the high temperature measurement of E up to 1025 ◦C;for each pair a p-value is shown, p < 0.05 indicates a significant difference

Porosity level / % 13.99 14.33 16.31 17.84 21.72

14.33 3.4e-05 - - - -16.31 0.0255 0.1164 - - -17.84 3.6e-08 0.0108 6.1e-05 - -21.72 0.1164 0.0025 0.0220 3.4e-06 -31.60 5.2e-16 1.6e-14 1.1e-13 1.9e-08 9.9e-11

temperature) [Franklin and Tucker, 1995]. This analysis supports the visual evaluation

of the results seen in Figure 4.10a. There were clearly significant differences between

most pairs of porosity. However, there were no significant differences within the pairs of

porosity level 13.99 %− 21.72 % and 14.33 %− 16.31 %.

4.1.5. Discussion

The presented results clearly showed a characteristic behavior of Young’s modulus in

dependence on the temperature. There was a standard linear decrease in stage one,

which can be found for most oxide ceramics [Wachtman et al., 1961]. However, the

most interesting observation was the strong increase of E within stage two at heating.

This somewhat exponential behavior was characterized by ending slightly above the for-

mer pyrolysis temperature. XRD measurement of the material prior and after the high

temperature Young’s modulus measurement did not reveal any changes in the phase

composition. Therefore, no phase transformation occurred and could contribute to that

increase of E.

A second possible mechanism which could contribute to an increase of E could be sinter-

ing. However, all tested compositions were already subjected to their former pyrolysis

temperature, which was always higher as the exponential E increase. Furthermore, tem-

peratures below 1000 ◦C are not sufficient for the sintering of alumina with a maximum

particle size up to 0.6 mm. Thus, sintering also can be excluded in this consideration.

Since the described mechanisms could be excluded, there were other possible microstruc-

tural changes within the material. For example a microcrack healing of the composites’

structure as well as of the single alumina and graphite constituents, within this stage

could be a contribution to the observed effect of E increase [Eto et al., 1991; Case et al.,

1981]. All the single materials expand in a different amount while heated up. The ther-

mal expansion coefficient (CTE) of graphite depends on the orientation of its crystal


layers. In layer direction it is negative below 400 ◦C and increases slightly up to 1450 ◦C,

while in perpendicular direction a CTE of 25× 10−6 to 42× 10−6 K−1 can be found for

the same temperature range [Pierson, 1993b]. The CTE of the used tabular alumina is

approximately 7 × 10−6 to 9 × 10−6 K−1 (own measurement). For the carbonized resin

a CTE from 3.2 × 10−6 to 6.9 × 10−6 K−1 depending on the resin and the preparation

route was obtained by Iacono et al. [2007]. For alumina and graphite the values of the

CTE are valid in a temperature range between 25 ◦C to 1450 ◦C. The glassy carbon

values were investigated up to 1000 ◦C. Regarding these big differences in the thermal

expansion behavior, the assumption of a contribution of this CTE mismatch to the high

temperature Young’s modulus behavior is self-evident.

Stage three (above the former pyrolysis temperature and the soak time) showed a slight

decrease of E and during the soak time a significant increase. This decrease can be

attributed to the beginning of a grain boundary sliding of the alumina, observed already

by Wachtman and Lam [1959] and described by Chang [1959]. It could be assumed that

first sintering stages contributed to the increase of E, observed for all compositions at

the soak time. The small shrinkage found in the expansion measurement supports this

assumption. A similar phenomena was mentioned by Baudson et al. [1999] for carbon-

bonded magnesia. The differences found for the soak time (lower E increase for higher

binder amount) could be due to the binder inhibiting the bridging of the alumina.

The hysteresis found between heating and cooling behavior supports the theory of mi-

crostructural changes in the material due to the thermal expansion mismatch. Ap-

parently, the microstructure was remarkably disturbed, since the Young’s modulus was

decreased irreversibly at the end of a measurement.

Figure 4.11 presents a schematic principle of the imagined microstructural changes within

one measurement cycle. Several authors already observed related phenomena and the

model to be presented here can be regarded as a summary of those preexisting literature

models [Li and Rigaud, 1993; Franklin and Tucker, 1995; Buchebner et al., 2008; Ham-

pel, 2010].

The material is composed of coarse alumina and graphite particles and a matrix (con-

taining graphite, glassy carbon and fine alumina particles). During cooling, after the

pyrolysis (shown in Figure 4.11a) the coarse alumina particles and graphite flakes de-

tach from the surrounding matrix, due to the significant lower CTE of glassy carbon

compared to alumina and natural graphite. Furthermore, the anisotropic expansion of

graphite flakes could contribute to this effect. This process leads to a very heterogeneous

microstructure comprised of many microcracks.


(a) Microstructure after the pyrolysis (b) At former pyrolysis temperature

(c) Above former pyrolysis temperature (d) after holding time

(e) At the stage of particle detachment (f) Room temperature after the measurement

Fig. 4.11.: A summarizing model of the assumed microstructural changes within the carbon-bondedalumina during a measurement of E(T ) based on theories proposed earlier by several authors [Buchebneret al., 2008; Li and Rigaud, 1993; Franklin and Tucker, 1995; Hampel, 2010]


While heated again within the measurement the alumina particles expand faster than

the surrounding matrix, resulting in a closure of the preexisting crack or gap. Thus,

Young’s modulus of elasticity increase significantly up to the state of pyrolysis (Figure

4.11b).

Increasing the temperature above the former pyrolysis temperature, results in a further

cracking of the microstructure. This is due to an extensive expansion of alumina as well

as graphite and leads to lower E values (Figure 4.11c). The significant increase of E at

the holding time is related to first sintering stages.

The decrease of E during cooling is attributed to the detachment of the grains from the

surrounding matrix (Figure 4.11e). This occurs suddenly.

At room temperature the gap between the grains and the surrounding matrix is bigger

than before, due to the ongoing expansion above the former pyrolysis temperature. This

leads to lower E values compared to the initial ones for all carbon-bonded compositions.

The results of the cycling experiment support the theory of matrix expansion due to

the thermal expansion of the single components. Once the pyrolysis temperature was

exceeded, the matrix was expanded, leading to greater gaps between the alumina grains

and the matrix. The delayed increase of E within each new cycle also supports the

theory of gap closing or healing, due to this further expansion of the matrix.

The results of the oxidation experiment emphasize the influence of this gap closure de-

scribed above. Despite the oxygen attack beginning at 400 ◦C, Young’s modulus was

increased again after a short period of decreasing due to oxidation. This recurring in-

crease clearly could be attributed to the gap closure between the matrix and alumina.

At the former pyrolysis temperature Young’s modulus was found to be at the same level

as initially. Afterwards, the oxygen attack became apparent and further contributed to

a decrease of Young’s modulus down to 80 % of its original value.

Besides the described similar behavior, there was a clear influence of the binder content,

binder amount, the pyrolysis temperature and the porosity on the high temperature

Young’s modulus. An increase of the binder content resulted in a reduced maximum of

E and a lower increase during the soak time as well as a decrease of the residual E. In

terms of the model described above, the amount of matrix was increased and less coarse

particles were present. Thus, the detachment of these particles from the matrix was less

after the pyrolysis, resulting in a smaller increase of E during reheating. Furthermore,

the bigger amount of binder phase reduced the contact possibilities of the alumina par-

ticles, leading to a smaller increase of E during the soak time.

Apparently this sintering related increase of E also contributes to the cooling behavior.

The particle detachment related decrease of E at cooling started at higher temperatures


for the high binder amount composition. Therefore, it is likely that the preliminary sin-

tering effects determined the temperature at which the coarse alumina particles detach

from the matrix or possibly even from each other. The residual E-value after one cycle

also correlated with this soak time increase of E. The higher this observed increase was,

the higher was the residual E. Thus, these sintering effects contributed to a stiffening of

the microstructure. Taking the thermal expansion measurements into account, a signif-

icant lower expansion behavior of the high binder amount composition was found. This

showed the influence of the binder phase and a reduced contribution of the alumina to

the overall composite expansion. Furthermore, above the former pyrolysis temperature

the lower binder amount composition showed an increased CTE which was not observed

for the high binder content material. This supports the model described above and shows

the significant influence of the binder.

The influence of the binder type was not as remarkable as for the binder amount. The

overall high temperature Young’s modulus behavior was similar for both compositions.

However, for the Carbores® bonded material the maximum E values were found to be

higher than for the resin bonded material. The behavior during the soak time was equal,

which is supporting the results regarding the binder content since the amount of binder

was equal and only the type was changed. Therefore, it can be concluded that the change

from the resin to the Carbores® binder only contributed to an increase of E above the

former pyrolysis temperature.

The thermal expansion measurements were in accordance with this model. In Figure

4.12 the thermal expansion of composition T20 is shown as an example of a thermal

expansion coefficient change below and above the former pyrolysis temperature. It can

be seen that all compositions showed a higher CTE above the former pyrolysis tem-

perature than below (see CTE values in the table of Figure 4.12). This confirms the

Young’s modulus measurement and the explanatory model. Above the former pyrolysis

temperature the material expands faster since all gaps were closed. Below the expansion

of the constituents was kind of absorbed due to gaps and microcracks.

The results of the pyrolysis temperature experiment strongly support the described

model. The higher the temperature of the preliminary pyrolysis was, the later (at

higher temperatures) the strong increase of E during heating was observed. The ab-

solute Young’s modulus at the maximum temperature was found to be almost similarly

independent of the pyrolysis temperature. Furthermore, the amount and slope of the

increase of E was higher, the higher the pyrolysis temperature was. Thus, the gaps

between coarse particles and the matrix increased with increasing pyrolysis temperature

and were correspondingly closed at the former temperature. Also the residual E was


0 500 1000 1500

0.0

0.5

1.0

1.5

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

(l − l0) l0α75−825α1025−1450

Composition α25−825 α1025−1450×10−6 K

T20 7.52 14.1T20-C 5.16 7.19T20-B10 4.93 6.08T20-3 4.90 10.9

Fig. 4.12.: Thermal expansion of T20 (6 wt % resin, 0.6 mm alumina particle size and 20 wt % graphite)is shown, the dotted lines are approximations of the coefficient of thermal expansion below and abovethe former pyrolysis temperature; In the table on the right the expansion coefficients above and belowthe former pyrolysis temperature of the investigated compositions are shown


influenced by the pyrolysis temperature. According to the model theory, the highest py-

rolized composition should comprise the smallest Young’s modulus decrease. The reason

therefore is the matrix which was expanded during the pyrolysis up to a temperature

of 1400 ◦C, which is approximately the maximum measurement temperature of 1450 ◦C.

This result was confirmed by the Young’s modulus measurement as well as by the thermal

expansion results. The overall expansion correlated directly with the pyrolysis tempera-

ture. The lower the pyrolysis temperature was, the higher was the expansion. Again, the

1400 ◦C treated composition did not expand as strong as the lower ones, because during

the preliminary pyrolysis the matrix was already stretched. Therefore, at reheating the

expansion was significant lower. Furthermore, the expansion velocity correlated directly

with the Young’s modulus measurement. The higher the former pyrolysis was, the later

an increase of the expansion speed was investigated. This increase was attributed to the

gap closing described above. The pyrolysis temperature did not affect the behavior dur-

ing the soak time. This confirms the results of the binder amount comparison, because

there was only a change in the pyrolysis temperature but not in the composition.

For the following considerations an equal pore structure in all samples is assumed, due

to the variation of the molding pressure as the exclusive factor of porosity variation.

The observed relation between Young’s modulus and porosity at room temperature can

be considered as almost linear (see Figure 4.9). All three models are sufficiently rep-

resenting the experimental data according to their R2 values. (see Table 4.6). The

R2-values of the well known models by Spriggs [Spriggs, 1961] (R2 = 0.9195) and Phani

[Phani and Niyogi, 1986] (R2 = 0.9071) indicate a good agreement of the model fit with

the data. Despite the composite nature of this carbon-bonded alumina material these

models might be applied for the calculation of E. However, the influence of the maximal

particle size, graphite and binder phase on Young’s modulus should be considered as

described above. Therefore, the stated estimates E0, b and m (see Table 4.6) may be

valid just for the described material.

The linear model seems to fit the data well at room temperature (R2 = 0.9078). However,

in terms of the model regarding E(T ) described above, the porosity could be regarded

as being reduced during heating. The highest observed value of E in this investigation

was 24 ± 2 GPa (for the 130 MPa samples) at 1225 ◦C. Certainly, other effects might

contribute to this result, but porosity reduction (or gap closure) could be regarded as

the most important one. Therefore, the data of the high temperature measurement of E

in dependence on the porosity indicated that the E0 = 15.26 GPa estimate of the linear

model at room temperature must be too low. Thus, the linear model fitted to the data

can not be considered as valid outside the measured porosity range.


Tab. 4.6.: Model functions and the obtained model parameters for the experimental E(P ) data; E0

represents the Young’s modulus at zero porosity; z, m and b are empirical constants

Model Estimate R2 ReferenceE0 Factor

E = E0 − zP 15.26 46.88 0.9078 -E = E0e

−bP 23.40 −6.97 0.9195 Spriggs et al.[Spriggs, 1961]E = E0(1− P )m 20.65 0.40 0.9071 Phani et al. [Phani and Niyogi, 1986]

As stated in the results section there was an influence of the porosity as well as of the tem-

perature on the Young’s modulus. A suitable model for this relationship was proposed

by Munro [Munro, 2004]. Porosity and temperature are assumed to be independent

variables in this case.

E(T, P ) = ET (T )EP (P ) (4.1)

Applying this approach to the data obtained in this investigation resulted in:

E(T, P ) = E0ea1T+a2T 2

ea3P (4.2)

where E0 = 29.844 GPa represents the Young’s modulus at room temperature and zero

porosity. a1 to a3 are empirical factors with a1 = −2.096 × 10−4 ◦C, a2 = 1.113 ×10−6 ◦C2, a3 = −8.324. The adjusted-R2-value for this model was found to be R2 =

0.9607. This indicates an excellent agreement with the measured data as shown in

Figure 4.13. However, this model only represents the data up to 1025 ◦C. For higher

temperatures a polynomial of higher order may be applied.

In terms of thermal shock resistance and the concepts used these days, the obtained

results are very interesting. The Young’s modulus at 1450 ◦C or more precisely at tem-

peratures above the former pyrolysis temperature, differs significantly from the room

temperature values. Also the change of binder amount, type or pyrolysis temperature

has a significant influence on the Young’s modulus at high temperatures. It is not pos-

sible to conclude from the room temperature elasticity to the high temperature elastic

behavior. However, it was shown that at least the porosity does not influence the rel-

ative Young’s modulus behavior at high temperatures which would allow to conclude

from room temperature E to high temperature E values.


● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●●

●●

●●

0 200 400 600 800 1000

05

1020

Temperature / °C

Youn

g's

mod

ulus

/ G

Pa

Porosity 13.99 %

● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●●

●●

● ●

0 200 400 600 800 1000

05

1020

Temperature / °C

Youn

g's

mod

ulus

/ G

Pa

Porosity 14.33 %

● ● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●●

●●

●

0 200 400 600 800 1000

05

1020

Temperature / °C

Youn

g's

mod

ulus

/ G

Pa

Porosity 16.31 %

● ● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●●

●● ●

0 200 400 600 800 1000

05

1020

Temperature / °C

Youn

g's

mod

ulus

/ G

Pa

Porosity 17.84 %

● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●

●●

●● ● ●

0 200 400 600 800 1000

05

1020

Temperature / °C

Youn

g's

mod

ulus

/ G

Pa

Porosity 21.72 %

Fig. 4.13.: Measured Young’s modulus E plotted versus temperature T at different porosity levels Pcompared to the introduced model (solid line)


Tab. 4.7.: The factorial design for the investigation of the influence of graphite content and maximumparticle size on the elastic and additional properties

Factor − +

A - Graphite content / wt %0 1010 30

B - Particle size / mm 0.045 3

4.2. Reference compositions

4.2.1. Influence of the maximum alumina particle size and the graphite

content

Room temperature investigation

In this section the influence of the composition (particle size and graphite content) on

the elastic properties was investigated. Therefore, the maximum alumina particle size

was varied in three steps (0.045 mm, 1 mm, 3 mm). The graphite content was changed

in 4 steps (0, 10, 20, 30 wt%).

In order to obtain the most important information and probable interactions between

both factors, the analysis of the results were categorized by 2 factors with 2 levels each (22

factorial design as shown in Table 4.7). Therefore, maximum particle sizes of 0.045 mm

and 3 mm were considered as factor levels, whereas the 1 mm composition was omitted

in the analysis. The graphite content levels were split up into 0 to 10 wt % and 10 to

30 wt %. The 20 wt % level was omitted. However, complete confidence plots are shown

in the appendix A.1.1 and A.1.2.

The effect of the factors will be illustrated by using bar charts showing the deviation of

the factor mean from the overall mean of the response variable. The significance of these

effects will be illustrated by dotted horizontal lines representing the confidence interval

of the effect for p < 0.05. An effect needs to be bigger than these confidence borders in

order to be regarded significant. A porosity after the pressing was calculated to obtain a

possible influence of the graphite addition in the compaction behavior during pressing.

The following equation was used for the calculation:

πP =

(1−

ρbgρt

)∗ 100 (4.3)

where ρbg is the bulk density after pressing (calculated by using the sample dimensions)

and ρt is the theoretical density of the material.


A B AB

effe

ct /

%

−15

−10

−5

05

1015 (A) Graphite content

(B) Maximum particle size(AB) Interaction

(a) 0 − 10 wt %

A B AB

effe

ct /

%

−15

−10

−5

05



(b) 10 − 30 wt %

Graphite content / %

Por

osity

afte

r pr

essi

ng /

%

0 10

510

1520

2530 max. particle size

0.045 mm3 mm

(c) Means and confidence inter-valls for 0 − 10 wt %

Fig. 4.14.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the appar-ent porosity after the pressing of the reference compositions, the dotted horizontal lines represent theconfidence levels

In Figure 4.14 the effects of increasing either the graphite content (0 − 10 wt % or

10−30 wt %) or the maximum alumina particle size (from 0.045−3 mm) on the porosity

after pressing are shown. First of all both factors and their interaction can be considered

significant because they were found to be bigger than the confidence level. However, the

strongest influence on the porosity after pressing clearly was factor B the maximum

particle size. Increasing the particle size resulted in a remarkably decreased porosity

after pressing. The graphite addition also decreased the porosity, however considerably

less. According to Oshima and McCarty [2012] ”an interaction effect exists when the

effect of one independent variable on the dependent variable depends on the value (level)

of some other independent variable included in the study design.”Regarding Figure 4.14c

helps to understand this. Both main effects can be analyzed globally because the effect

direction still remained the same. A small interaction effect of the graphite content on

the effect of maximum particle size could be seen. Increasing the graphite content had a

slightly reducing effect on the effect of increasing the maximum particle size. However,

this effect was very small compared to the main effect of factor B. Thus, the conclusion

that both factors had a reducing effect on the porosity after pressing is correct.

Exactly the same effects were observed for the apparent porosity after the pyrolysis

(see Figure 4.15). The effect of the graphite increase from 0 − 10 wt % was slightly

increased. However, the influence of the maximum particle size was still approximately

three times bigger than for the change in the graphite content (independent of the level).

Furthermore, a significant interaction was found in the graphite range from 10−30 wt %.

In Figure 4.15c it can be seen that the effect of increasing the maximum particle size


A B AB

effe

ct /

%

−15

−10

−5

05



(a) 0 − 10 wt %

A B AB

effe

ct /

%

−15

−10

−5

05



(b) 10 − 30 wt %


App

aren

t por

osity

afte

r th

e py

roly

sis

/ %

10 30

1015

2025


0.045 mm3 mm


Fig. 4.15.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the appar-ent porosity after the pyrolysis of the reference compositions, the dotted horizontal lines represent theconfidence levels

was reduced due to the increase of factor B , the graphite content. Nevertheless, the

main effect conclusions still remain valid.

Therefore, the porosity of these materials was determined by the pressing process, which

was remarkably influenced by the maximum alumina particle size. The graphite content

had less influence on the compaction behavior. This porosity difference has to be taken

into account for the discussion of the elastic properties.

Considering the bulk density in Figure 4.16, the influence of the two factors were found

to be similar according to the changes in the porosity, however vice versa. Increasing the

maximum particle size resulted in a strong increase of the bulk density of approximately

0.4 g/cm3. Of course the increase of the graphite content resulted in a decrease of

the bulk density due to the lower density of graphite compared to alumina, which was

substituted by the graphite. Again there was an interaction (see Figure 4.16c). The

effect of increasing the maximum particle size on the bulk density was reduced at the

upper level of the graphite content. Concluding, the bulk density was increased by the

increase of the maximum particle size. However, this effect depended on the graphite

level. Above 10 wt % this effect might be decreased due to the graphite addition

The results of the two factorial comparisons of the Young’s modulus are shown in Figure

4.17. The 0− 10 wt % graphite experiment in Figure 4.17a revealed clear significance of

the two main effects and the interaction of both. Therefore, the confidence plot in Figure

4.17c was introduced to prevent erroneous conclusions. The two main effects showed a

strong reducing effect on the Young’s modulus. The biggest impact was found to be


A B AB

effe

ct /

g cm

−3

−0.

4−

0.2

0.0

0.2

0.4

(A) Graphite content(B) Maximum particle size(AB) Interaction

(a) 0 − 10 wt %

A B AB

effe

ct /

g cm

−3

−0.

4−

0.2

0.0

0.2

0.4


(b) 10 − 30 wt %


Bul

k de

nsity

/ g

cm−3

10 30

2.2

2.3

2.4

2.5

2.6

2.7

2.8

max. particle size

0.045 mm3 mm


Fig. 4.16.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the bulkdensity of the reference compositions, the dotted horizontal lines represent the confidence levels

factor B, the maximum particle size. Regarding the confidence plot in Figure 4.17a the

influence of factor B, the maximum particle size, always showed the same effect direction

(reducing E). Therefore, it can be concluded that the maximum particle size increase

was accompanied by a decrease of E in the graphite range of 0−10 wt %. Unfortunately,

there was no such a global conclusion for the graphite content. Its effect on E clearly

depended on the level of the maximum particle size. At the small particle size level,

an increase of the graphite content significantly reduced the Young’s modulus, whereas

there was no significant effect found at the high particle size level.

In case of a graphite variation of 10−30 wt %, there was no significant interaction found.

In Figure 4.17b the two main effects were significant. Thus, the increase of the graphite

content at a constant particle size level resulted in a decrease of E. Furthermore, the

increase of the maximum particle size showed a decrease of E, too. The absolute effects

on E were remarkably smaller than for the 0− 10 wt % step comparison. Therefore, the

effects of changing the maximum particle size or the graphite content on the Young’s

modulus were decreased by increasing the graphite content.

Concluding, the increase of the maximum alumina particle size was accompanied by a

decrease of Young’s modulus in both observed graphite ranges. The impact of this effect

was greatest when changing from a zero graphite composition to a 10 wt % composition.

The addition of more graphite did not enforce this effect. The influence of the graphite

content was dependent on the maximum particle size at the low graphite levels 0 −10 wt %. At higher levels (10− 30 wt %) the graphite addition also caused a reduction of

E, whereas no such influence was found in the low level experiment.

In Figure 4.18 the results for the shear modulus are shown. Clearly, the effects were


A B AB

effe

ct /

GP

a

−6

−4

−2

02

46


(a) 0 − 10 wt %

A B AB

effe

ct /

GP

a

−6

−4

−2

02

46


(b) 10 − 30 wt %

Graphite content / wt%

Youn

g's

mod

ulus

/ G

Pa

0 10

510

1520


0.045 mm3 mm


Fig. 4.17.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the Young’smodulus of the reference compositions, the dotted horizontal lines represent the confidence levels, theconfidence plot in (c) might support the interpretation of the interaction effect found in a)

smaller in absolute values than for the Young’s modulus, but the tendency was the same

as for the graphite change of 0−10 wt %. Again the interaction was significant, resulting

in a more differentiated analysis shown in Figure 4.18c. The results are exactly the

same as for the Young’s modulus. No effect was found by changing the particle size at

a graphite level of 10 wt % and also by changing the graphite at a particle size of 3 mm.

However, the results of the 10 − 30 wt % experiment were different to the Young’s

modulus results. Again there was no significant interaction. The increase of graphite

from 10− 30 wt % showed the strongest effect on the shear modulus which was reduced.

The increase of the maximum particle size also had a reducing effect on G, which however

was significant lower than the effect of the graphite content. This might influence the

results of the Poisson’s ratio since it is calculated by those two variables.

The influence on Poisson’s ratio of the graphite amount and the maximum particle size

is shown in Figure 4.19. In case of changing the graphite content from 0− 10 wt % there

was no significant effect observed; neither for the graphite amount nor the particle size.

However, according to the differences in shear and Young’s modulus described above,

there was a significant influence of the graphite content on Poisson’s ratio found for

the graphite content range of 10− 30 wt %. Within this border, increasing the graphite

amount resulted in a significant increase of Poisson’s ratio.

The damping behavior and its response to the change of graphite content and maximum

particle size is shown in Figure 4.20. From 0 − 10 wt % graphite both factors and their

interaction were significant. The strongest influence on the damping showed the graphite


A B AB

effe

ct /

GP

a

−6

−4

−2

02

46


(a) 0 − 10 wt %

A B AB

effe

ct /

GP

a

−6

−4

−2

02

46


(b) 10 − 30 wt %


She

ar m

odul

us /

GP

a

0 10

24

68


0.045 mm3 mm


Fig. 4.18.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the shearmodulus of the reference compositions, the dotted horizontal lines represent the confidence levels

A B AB

effe

ct

−0.

2−

0.1

0.0

0.1

0.2


(a) 0 − 10 wt %

A B AB

effe

ct

−0.

2−

0.1

0.0

0.1

0.2


(b) 10 − 30 wt %

Fig. 4.19.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the Poisson’ratio of the reference compositions, the dotted horizontal lines represent the confidence levels

A B AB

effe

ct

−0.

002

−0.

001

0.00

00.

001

0.00

2


(a) 0 − 10 wt %

A B AB

effe

ct

−0.

002

−0.

001

0.00

00.

001

0.00

2


(b) 10 − 30 wt %


Dam

ping

0 10

0.00

40.

006

0.00

80.

010

max. particle size

0.045 mm3 mm


Fig. 4.20.: Effect of the graphite content and maximum particle size (0.045 mm to 3 mm) on the Dampingof the reference compositions, the dotted horizontal lines represent the confidence levels


content, followed by the maximum particle size. Regarding the confidence plot in Figure

4.20c, there was no effect of the particle size on the damping at zero graphite content.

Nevertheless, the increase of the graphite content always was accompanied by higher

damping values. Furthermore, at the 10 wt % graphite level the maximum particle size

variation from low to high caused an increase of the damping.

The results of the 10−30 wt % graphite comparison confirmed this observation. The two

main factors showed significant effects on the damping of the material. The strongest

impact was the maximum particle size change.

Discussion

The results presented above clearly showed the influence of the graphite content and

maximum alumina particle size on the elastic and other physical properties of carbon-

bonded alumina. First of all, the increase of the maximum particle size showed the most

relevant effect on the compaction behavior. Increasing the particle size resulted in a bet-

ter compaction, lower apparent porosity and higher bulk density. The reason therefore

clearly was the better particle size distribution of the coarse particle composition com-

pared to the small particle size composition (see Table 3.2). The graphite content also

had a positive effect on the pressing process. Hence, it can be regarded as a lubricant.

Furthermore, there was an interaction between these two factors. This means changing

the levels of both factors resulted in a dependence of either the effect of graphite content

change on the particle size change or vice versa.

The elastic properties (E, G, ν and damping) responded remarkably on the two factors.

The Young’s modulus was clearly influenced by both factors. Furthermore, there was

an interaction found. The influence of the pressing process on these results has to be

considered. At the small particle size level an increase of the graphite from 0− 10 wt %

content resulted in a decrease of E and G. Furthermore, ν was not influenced. This

result is in good agreement with the theory regarding the Young’s modulus of composite

materials presented in section 2 since E and G of graphite are significantly lower than

those of alumina. However, at the high particle size level the effect of graphite addition

was almost contrary. A reason therefore could be the different particle size distribution

of both compositions. A lower apparent porosity might contribute to this effect. There-

fore, the effect of graphite addition was depended on the level of the maximum particle

size at low graphite contents.

At higher graphite contents of 10− 30 wt % the interaction was not significant anymore.

Increasing the graphite content resulted in a decrease of E and G. The decrease of the


elastic properties due to the particle size increase is hard to explain since the apparent

porosity was decreased within the same graphite content range. The decrease due to

the graphite addition can be explained easily by the mixture laws introduced earlier

(see section 2). Furthermore, the introduction of microcracks due to a different abso-

lute expansion of the small and coarse alumina grains might be one explanation for the

reduction of E and G with increasing particle size. Besides, Poisson’s ratio responded

significantly on the addition of graphite above 10 wt %. This also can be explained with

the increasing amount of a second phase in this composite material.

The damping responded significantly on the graphite content change as well as on the

maximum particle size. Again there was found a significant interaction for the low

graphite content experiment. This was due to the lack of a maximum particle size influ-

ence on the damping at zero graphite content. At higher graphite contents both factors

(graphite content and maximum particle size) were significantly influencing the damping

behavior. It was assumed that only internal damping was measured (damping related to

the microstructure). The introduction of either graphite or bigger particles caused an in-

crease of grain boundaries or at least a change of the former grain boundary state. Thus,

vibration energy was more dissipated due to the graphite introduction. Furthermore,

the bigger particles could introduce microcracks due to their stronger absolute thermal

expansion during pyrolysis. All these microstructural processes could contribute to the

damping effects shown above [de Silva, 2005].

Comparing the obtained results with the composite-model of Hashin and Shtrikman

[1963] could contribute to a better predictability of the elastic properties of carbon-

bonded alumina. Therefore, the Hashin and Shtrikman Bounds (HS) were calculated

for the reference compositions. However, these bounds provide only a two-phase model,

whereas the carbon-bonded alumina is a three phase material. Therefore, at first the

composite E of the two-phase material alumina-glassy carbon was calculated. There-

after, this alumina-glassy carbon two phase composite was regarded as one phase and

a second phase, graphite, was added to the model. The alumina-glassy carbon E value

from the first calculation was then used as one phase E. This is the reason for the

discrepancy of upper and lower HS-bounds at zero graphite content, since they actually

represent the bounds for an alumina-glassy composite.

The results of this calculation are shown in Figure 4.21. The upper as well as the

lower bounds were very far away from the measured results. Considering Figure 4.21b,

the measured E values did not show a comparable dependence on the graphite content

as the calculated values did. However, the porosity differences of the samples discussed

above, contributed to this result. The porosity was directly correlated to the graphite


●

●

●

●

0 5 10 15 20 25 30

010

020

030

040

0


Youn

g's

mod

ulus

/ G

Pa

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

upper HS−Boundlower HS−Bound

(a) HS-bounds

●

●

●

●

0 5 10 15 20 25 30

050

100

150

200

250

Graphite content / %Yo

ung'

s m

odul

us /

GP

a

●

●

●

●

●

●

●

●

●● ● ●

● ● ● ●● ● ● ●

●

●

lower HS−Boundmeasured E

(b) Lower HS-bound and mea-sured Young’s modulus

0 5 10 15 20 25 30

05

1015

20


Em

piric

al p

aram

eter

b

● ● ●

●

●

0.045 mm1 mm3 mm

(c) Calculated parameter b

Fig. 4.21.: Calculated HS-bounds compared to the measured E of the reference compositions; in (c) thecalculated b parameter according to Spriggs in dependence on the maximum particle size is shown

content. The higher the graphite content was, the lower was the apparent porosity. The

calculated HS-bounds did not take the porosity into account. Therefore, the porosity

influence on the E values can be clearly seen here. Furthermore, the existence of microc-

racks within the composition, certainly contributed to the discrepancy of theoretical and

measured values. It also has to be considered that the HS-bounds were established for

homogeneous material, which is clearly not the case for the investigated compositions.

Applying Spriggs’s model (see Table 2.2) to the measured and calculated E values, offers

the opportunity to compute the b parameter in dependence on the graphite content. In

Figure 4.21c this parameter is shown in dependence on the graphite content and the

maximum particle size of the composition. Besides the exception of 20 wt % graphite

content and 3 mm particle size, it could be said that the parameter b was almost inde-

pendent on the graphite content. However, a dependence on the maximum particle size

was found. As discussed in chapter ”State of the art”, the pore shape plays an important

role in the relationship of Young’s modulus and porosity. Therefore, it could be assumed

that the observed particle size influence might be attributed to differences in the pore

shape within the compositions. This could be caused by the differences in the particle

size distribution and maximum particle sizes. In conclusion, this calculation showed

clearly the contribution of the pore shape on the Young’s modulus dependence on the

porosity.


High temperature investigation

The results of the high temperature investigation are illustrated in the same way as in the

previous section 4.1 ”Industry related compositions”. The Young’s modulus difference of

ET − E0 was normalized to its room temperature value E0. Furthermore, the thermal

expansion of the compositions and the behavior of the samples during the holding time

(E − Ei normalized to Ei the initial E at the holding time) are shown.

The results of the high temperature measurements for the 0.045 mm compositions are

shown in Figure 4.22. The Young’s modulus measurement results up to 1450 ◦C are

shown in Figure 4.22a. E increased significantly up to the former pyrolysis tempera-

ture of 1000 ◦C during heating. Above this temperature E remained almost constant.

The graphite content contributed significantly to this increase. The graphite containing

compositions showed an almost 2 to 3 times higher increase of E than the zero graphite

composition with a total increase of ≈ 30 %. There was no significant relationship be-

tween the total increase and the graphite amount. The highest increase of E was found

for the 20 wt % graphite composition (E − E0/E0 ≈ 75 %), whereas there was almost

no difference between the 10 and 30 wt % graphite compositions which were between the

20 wt % and zero wt % graphite compositions.

During soaking a strong increase of E was found (see Figure 4.22c). The carried out

ANOVA revealed a significant influence of the time on E and no influence of the graphite

content on E (see Table A.14 in the appendix).

During cooling all compositions showed a hysteresis behavior. Down to temperatures

between 600 and 800 ◦C E remained almost constant and above the values reached dur-

ing heating. Below these temperatures E decreased significantly to room temperature.

Depending on the graphite content the residual Young’s modulus was equal or higher

than the initial value (20 and 30 wt % compositions) or lower for the zero and 10 wt %

composition.

The results of the thermal expansion measurement are shown in Figure 4.22b. Unfor-

tunately the result of the 10 wt % composition measurement got lost due to an energy

shutdown during the measurement. Up to approximately 1250 ◦C the expansion behavior

of all compositions can be regarded as equal. Above this temperature the compositions

started to show a reduced expansion in dependence on the graphite content. The higher

the graphite content the less was the reduction in expansion. In other words the strongest

total expansion was found for the highest graphite content. The zero graphite compo-

sitions showed an unusual expansion during soaking. There could be several possible

reasons for this phenomenon. The most reasonable would be related to the heat dis-


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

0 wt%10 wt%20 wt%30 wt%


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

0 wt%20 wt%30 wt%


0 20 40 60 80 100 120

05

1015

Soak time / min

(E−

Ei)

Ei /

%

0 wt%10 wt%20 wt%30 wt%

(c) Soak time behavior

Fig. 4.22.: Young’s modulus and thermal expansion measurement up to 1450 ◦C of the 0.045 mm com-position


sipation within the testing apparatus. There was an alumina ring around the sample

filled with pet coke to protect the samples from oxidation. The thermocouple however

was assembled outside of this circle. Furthermore, the high porosity of the zero graphite

composition certainly caused a lower heat conduction in the material. Thus, the ongoing

expansion during the soak time of the zero graphite composition might be related to a

delay due to the reasons described. During cooling all compositions showed a linear

shrinkage.

In Figure 4.23 the results of the high temperature investigation of the 1 mm composi-

tion are shown. The Young’s modulus evolution in Figure 4.23a was the same as for

the industry related compositions pyrolized at 1000 ◦C. However, there was clearly a

significant influence of the graphite content on this behavior. The less graphite the

composition contained the stronger was the slope of E(T ) in the temperature range of

500− 1000 ◦. Additionally, Emax decreased with increasing graphite content. A sudden

decrease of E after the holding time was observed. This decrease was steeper for the

zero graphite composition than for the graphite containing ones. The overall reduction

of E was around 50 % for the 20 & 30 wt % graphite compositions and around 70 % for

the 0 & 10 wt % compositions.

The difference between 0 & 30 wt % graphite was around 70 % at the former pyrolysis

temperature, whereas there was no difference between 10 & 20 wt % at this temperature.

The thermal expansion behavior is shown in Figure 4.23b. Considering only the heat-

ing curves, a significant influence of the graphite on α(T ) was found. The higher the

graphite content was the more nonlinear was the heating curve evolution. For the higher

graphite compositions (20 & 30 wt %) the slope of the expansion increased strongly be-

tween 750 ◦C and 1000 ◦C. This might be due to the pyrolysis temperature of 1000 ◦C

which was also clearly visible in the E measurement.

During the holding time again there was a strong expansion found for the zero graphite

composition. The explanation was already given for the 0.045 mm composition.

The cooling curve behavior again was affected by the graphite content. For the non

graphite composition a linear decrease was found whereas the curves appeared to be

more nonlinear with increasing graphite content.

The Young’s modulus was not significantly dependent on the soak time (see Figure

4.23c). Furthermore, there was a strong scattering of the measurement data contribut-

ing to this result. However, the graphite content was determined as a significant factor

by the carried out ANOVA (see Table A.25). Therefore, a pairwise comparison was

additionally done to determine the differences between the compositions. The results

are shown in Table 4.8. There were significant differences found between 0-20 wt %, 0-


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

0 wt%10 wt%20 wt%30 wt%


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

0 wt%10 wt%20 wt%30 wt%


0 20 40 60 80 100 120

−2

02

46

810

Soak time / min

(E−

Ei)

Ei /

%

0 wt%10 wt%20 wt%30 wt%


Fig. 4.23.: Young’s modulus and thermal expansion measurement up to 1450 ◦C of the 1 mm composition


Tab. 4.8.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) for the graphite content influence on the soak time behavior of E for the 1 mmcompositions; for each pair a p-value is shown, p < 0.05 indicates a significant difference

0 10 20

10 0.1813 − -20 0.0205 0.0049 -30 0.0205 0.1813 0.1813

30 wt % and 10-20 wt % graphite compositions. Furthermore, a tendency of increasing

Young’s modulus could be seen for all compositions.

The results of the high temperature Young’s modulus measurement for the 3 mm com-

positions are shown in Figure 4.24a. The actual curve development was the same as for

all carbon-bonded compositions before. However, compared to the 1 mm composition

results the graphite content influence was different. The lowest increase of E during

heating was found for the zero and 20 wt % graphite compositions, whereas the highest

E values were found for the 30 wt % composition. The graphite content influence was

not as linear as for the 1 mm composition. Furthermore, the maximum ∆E was 175 %

for 30 wt % graphite and 130 % for 0 wt % graphite. This was significantly higher than

for the 1 mm compositions. A decrease of E of around 65 % (0,10,30 wt % graphite) and

50 % for the 20 wt % composition was observed after a measurement.

The thermal expansion up to 1450 ◦C is shown in Figure 4.24b. Again, the influence

of the graphite amount on the thermal expansion was quite obvious as for the 1 mm

compositions, too. The higher the graphite amount was, the lower was the obtained

maximum expansion at 1450 ◦C. Furthermore, the expansion during heating was more

nonlinear for the higher graphite amount compositions. The highest expansion was found

for the non graphite composition. The cooling behavior was comparable to the heating

curve since it turned more nonlinear with increasing graphite content resulting in a

residual expansion of the material (in case of extrapolating to room temperature). Once

again, an expansion during the holding time of the zero graphite composition occurred.

The reason therefore was already described for the 0.045 mm composition.

The soak time behavior can be found in Figure 4.24c. Clearly a dependence of E on the

graphite content was observed. The lower the graphite content was, the more apparent

was an increase of E during the holding time.

A significant mass loss and porosity increase during the high temperature E measurement

was observed for samples of all compositions. Therefore, several ANOVA were carried


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

0 wt%10 wt%20 wt%30 wt%


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Temperature / °C

(l−

l 0)

l 0 /

%

0 500 1000 1500

0 wt%10 wt%20 wt%30 wt%


0 20 40 60 80 100 120

−5

05

Soak time / min

(E−

Ei)

Ei /

%

0 wt%10 wt%20 wt%30 wt%


Fig. 4.24.: Young’s modulus and thermal expansion measurement up to 1450 ◦C of the 3 mm composition



(Ea

−E

i)E

i / %

0 10 20 30−

100

−50


0.045 mm1 mm3 mm

Fig. 4.25.: Young’s modulus change after the high temperature measurement in dependence on themaximum particle size and graphite content; where Ea represents E after the measurement and Ei

before, both at room temperature

out to investigate the dependence of this mass loss, the porosity increase and the Young’s

modulus change on the particle size and the graphite content (see paragraph A.1.1 for

exact ANOVA tables).

The graphite content as well as the particle size were found to be a significant influence

on the retained Young’s modulus after one measurement. Furthermore, the interaction of

both was significant, too. Due to the high amount of experiments, pairwise comparisons

were omitted. Instead, the means of Young’s modulus variation were plotted against

the graphite content (shown in Figure 4.25). Clearly, the significance of the particle size

influence can be observed. Furthermore, an influence of the graphite content was visible,

however the data scattering was quite high. Apparently, higher graphite contents led

to less Young’s modulus reduction. This was only true up to 20 wt % graphite. Above,

∆E/Ei was reduced. The particle size affected ∆E/Ei significantly, too. But only

the levels 0.045 mm and 1/3 mm differed significantly from each other. The coarser the

maximum particles were, the bigger was the observed Young’s modulus reduction after

one cycle.

The influence of the graphite content on the mass loss and the porosity was tested, too.

There was no significance found for the graphite content at the particle size levels of 1

and 3 mm. Only at a level of 0.045 mm the graphite content had a significant influence

on the retained mass and porosity. In Tables 4.9a and 4.9b the results of a comparison

of means are shown. Only the zero graphite content composition showed a significantly


Tab. 4.9.: Results of the multiple comparison of means ad-hoc test (Tukey-HSD) for the graphite contentinfluence on the retained porosity and mass loss after a high temperature measurement for the 0.045 mmcompositions; for each pair a p-value is shown, p < 0.05 indicates a significant difference

(a) Test for the porosity change

0 10 20

10 0.923 − −20 0.879 0.999 −30 0.001 0.002 0.002

(b) Test for the mass loss

0 10 20

10 0.018 − −20 0.0135 0.995 −30 0.0145 0.997 0.999

different mass change compared to the other compositions (0.60 % lower porosity change

compared to all other compositions). However, this tendency was not found for the

porosity change (see Table 4.9b) as it could be expected since the mass loss was assumed

to be caused by oxidation. Instead, the 30 wt % graphite composition exhibited a higher

porosity increase than the other compositions.

In conclusion it can be said, that the oxidation influence could be registered by a mass

loss. Nevertheless, a clear dependence of the retained Young’s modulus values on the

mass loss could not be demonstrated.

Discussion

In the discussion part of section 4.1, a model describing the high temperature changes

of E(T ) of carbon-bonded alumina was suggested. The results presented above will be

discussed according to that model.

Regardless of the graphite content and the particle size, an increase of E up to the

former pyrolysis temperature was observed for all compositions. Furthermore, a strong

hysteresis was found between heating and cooling. This behavior was explained earlier.

Due to preexisting gaps between the constituents, which were closed at reheating, E

increased. The hysteresis during cooling was explained by the occurrence of sintering

(stiffening effect) and stretching of the matrix (decreasing E) due to different thermal

expansion coefficients of the contained materials and temperatures above the former py-

rolysis temperature. The sintering effect was proved due to an increase of E during the

soak time and the occurrence of slight shrinkage during the holding time. Therefore, in

general the results of the reference compositions support the described model.

Nevertheless the approach of this study was to determine the influence of certain factors

on the high temperature Young’s modulus. Therefore, the graphite content and the

maximum particle size were introduced as factors. The influence of the graphite content

was shown above at each particle size level. It was no consistent relationship between the


Young’s modulus in dependence on the temperature and the graphite content found. At

the smallest particle size the non graphite material showed the lowest overall E increase

(also of all compositions). No significant difference was found for the graphite contain-

ing compositions between each other. Adding graphite to the composite reduces the

volume fraction of alumina and binder. Thus, a mismatch between the thermal expan-

sion coefficients of the material can be assumed and could contribute to microcracking

and gap development in the material. These gaps and microcracks could be assumed

to be numerously and even bigger than for the zero graphite composition. Therefore,

the Young’s modulus at reheating (during the measurement) increased strongly for the

graphite containing compositions at a particle size of 0.045 mm. However, the contri-

bution of the porosity to this behavior is not really understood yet. The results from

the section 4.1 suggest that the porosity influence on the normalized Young’s modulus

could be omitted within a porosity range of 14 to 21 %. The 0.045 mm compositions

had a porosity between 29 and 38 %. The range between highest and lowest porosity is

comparable. Therefore, a possible porosity influence was omitted in this discussion.

It might be assumed, that at the other particle size levels the same relationship will be

evident. However, different results were obtained. The 3 mm and zero graphite con-

taining composition also comprised the lowest increase of E up to the former pyrolysis

temperature. But, at a particle size of 1 mm and the same graphite level (zero), the

increase of E was the highest found at this particle size level. Furthermore, differences

between the graphite levels were found at these two particle size levels. These results

show that there was an interaction effect between the graphite content and the maximum

particle size. For example at a maximum particle size of 3 mm the strongest increase of

E was found for the 30 wt % graphite composition, whereas at a particle size of 1 mm

this graphite level caused the lowest E increase. According to the model suggested ear-

lier, the addition of graphite would disturb the microstructure bit by bit resulting in

a stronger increase of E due to the gap closure and crack healing. Nevertheless, too

much graphite apparently caused so many microcracks that they could not be com-

pletely closed during reheating. This might be one reason for the phenomena observed.

A second one could be the contribution of the particle size of the graphite. Alternating

the alumina particle size, changes automatically the relation between the graphite and

alumina particles. Therefore, the quite coarse graphite could exhibit more microcracks

within the composite material, whereas at a bigger alumina particle size, the graphite

could be better gathered in the gaps between the alumina particles.

Obviously, the maximum alumina particle size contributed significantly to the high

temperature Young’s modulus. In Figure 4.26 the previously shown results of the high


0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

3 mm1 mm0.045 mm

(a) 0 wt %

0 500 1000 1500

−50

050

100

150

Temperature / °C(E

−E

0)E

0 / %

0 500 1000 1500

3 mm1 mm0.045 mm

(b) 10 wt %

0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

3 mm1 mm0.045 mm

(c) 20 wt %

0 500 1000 1500

−50

050

100

150

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

3 mm1 mm0.045 mm

(d) 30 wt %

Fig. 4.26.: Young’s modulus measurement up to 1450 ◦C sorted by graphite content

temperature E measurement are sorted by the maximum particle size for each graphite

content level. Thus, it is easier to obtain an influence of the particle size on the high tem-

perature E. Clearly, the coarse particle containing compositions (1 and 3 mm) exhibited

steeper and higher increases of E up to the former pyrolysis temperature. Further-

more, the hysteresis between cooling and heating was different for the finest particle size

composition (0.045). Besides for the zero graphite composition there was almost no E

reduction during one cycle for these compositions. The 3 mm compositions showed the

strongest increase of E during heating and the steepest decrease during cooling. Besides

these differences the 3 mm and 1 mm compositions showed an almost equal high temper-

ature behavior.

Thus, the maximum particle size effect was greatest between 0.045 mm and 1 mm.

Coarser particles are expanding and shrinking more in absolute values than smaller

particles. Therefore, the coarse particle containing compositions might be regarded as

stronger disturbed before a measurement. Again these defects could be healed during

the reheating resulting in the strong increase observed. Also the strong decrease of the

residual E supports this theory.

The sintering of the compositions at the holding time can be regarded as proven. All of

the fine particle compositions showed a significant increase of E during the holding time,

supporting the sintering theory. Furthermore, with increasing particle size that increase

of E decreased until no effect for the 3 mm composition. Furthermore, this sintering

influenced the hysteresis behavior which can be seen in Figures 4.26a - 4.26d. The finest

particle size compositions were found to exhibit the strongest increase of E during soak-

ing. At cooling these compositions then showed higher values of E than during heating.

Only at graphite contents of 0 and 10 wt % the residual E was smaller than the initial.

Concluding, the introduced model from section 4.1 was proven by the results of the

reference compositions. Furthermore, a significant influence of the graphite content, the


maximum particle size and their interaction on the high temperature Young’s modulus

was obtained. The effect of the graphite content was influenced by the level of the max-

imum particle size. Therefore, a main conclusion of the influence of the graphite content

on E could not be made. However, there was a quite clear influence of the maximum

particle size on E up to 1450 ◦C. The finer the alumina particles were the lower was the

overall increase of E and the less strong was the hysteresis between cooling and heating.

Thus, the fine particles did not disturb the material during pyrolysis as strong as the

coarse particles.

Furthermore, a mild oxidation during a measurement was observed due to a mass loss of

the samples. This mass loss was not dependent on the graphite content of the samples

but on the particle size. This oxidation could not be avoided, however a clear influence

on the retained Young’s modulus could not be proven. Therefore, the shown results

above contain a contribution of this oxygen attack which has to be considered.

The thermal expansion measurement supported the results obtained already in the pre-

vious section. In Table 4.10 a shift of the thermal expansion slope in the temperature

range of 25 − 825 ◦C and 1025 − 1450 ◦C clearly was proven. This shift was dependent

on the graphite content as well as on on the maximum particle size. For the smallest

particle size of 0.045 mm the shift from a lower expansion coeffiecient to a higher above

the former pyrolysis temperature was reversed. Below the pyrolysis temperature α was

higher than above which shows the particle influence on the microstructure. For the

30 wt % graphite composition of this small particle size the expansion shift was found to

be positive as for all other compositions. Thus, the bigger graphite flakes influenced the

microstructure in a comparable way as the alumina particle. At the 1 and 3 mm particle

size the shift was always positive. With higher graphite contents the difference between

the expansion below and above the pyrolysis temperature increased. Therefore, again

the graphite particle size influenced the result due to higher microcracks which were

introduced during the pyrolysis. After closing these microcracks during reheating up to

the former pyrolysis temperature, the expansion coefficient increased strongly due to an

undisturbed expansion of the now ”defect free” composite. These results support greatly

the model suggested in section 4.1 and correlate to the results of the high temperature

Young’s modulus measurement.


Tab. 4.10.: Coefficients of thermal expansion below and above the pyrolysis temperature of 1000 ◦C independence on the graphite content and maximum particle size

max. particle size 3 mm 1 mm 0.045 mmα25−825 α1025−1450 α25−825 α1025−1450 α25−825 α1025−1450

Graphite content ×10−6 K−1 ×10−6 K−1 ×10−6 K−1

0 % 7.23 9.27 7.00 9.79 7.33 5.3310 % 5.95 6.70 6.16 9.05 − −20 % 4.10 7.44 4.35 9.22 7.00 6.2430 % 4.15 10.60 4.39 11.20 7.49 10.00

Tab. 4.11.: The factorial design for the investigation of the influence of carbon filler type and maximumparticle size on the elastic and additional properties, the used filler types were AF = fine natural graphite,NFL = coarse natural graphite, CB = carbon black and Mix = 1:1 AF/NFL

Factor − +

A - Carbon filler typeMix AFMix NFLMix CB

B - Particle size / mm 0.045 3

4.2.2. Influence of the maximum alumina particle size and the carbon filler

type

Since different types of carbon filler are applied often in the refractory industry, their

influence on the elastic properties was investigated, too. Therefore, three 22 full factorial

experiments were carried out (see Table 4.11). The maximum alumina particle size was

varied in three steps (0.045 mm, 1 mm, 3 mm). Four different carbon filler types were

investigated. Considering the filler type as a factor, the ”- level” was always defined as

”Mix” because this was the condition for all the previously discussed compositions. The

1 mm level of the particle size factor was omitted, though the results can be found in the

appendix A.1.2.

Comparison of fine graphite (AF) to AF/NFL mix (fine/coarse)

In Figure 4.27 the effects of changing the filler type on the apparent porosity and bulk

density are shown. Clearly, there was no effect of changing the carbon filler from a

mixture of fine and coarse graphite to the fine graphite on its own on the porosity

and the bulk density. Again, the effect of increasing the maximum particle size was a


A B AB

effe

ct /

%

−15

−10

−5

05

1015

(A) Carbon type(B) Maximum particle size(AB) Interaction

(a) Apparent porosity after thepressing

A B AB

effe

ct /

%

−15

−10

−5

05

1015 (A) Carbon type


(b) Apparent porosity after thepyrolysis

A B AB

effe

ct /

g cm

−3

−0.

4−

0.2

0.0

0.2

0.4


(c) Bulk density

Fig. 4.27.: Effect of the carbon filler type (AF) and the maximum particle size (0.045 mm to 3 mm)on the Apparent porosity and bulk density of the reference compositions, the dotted horizontal linesrepresent the confidence levels

reduction of apparent porosity and an increase of bulk density. This effect was already

found in the previous experiment described above.

Nevertheless, the elastic properties were influenced by both factors significantly (see

Figure 4.28). Surprisingly, the influence of the graphite filler was stronger than that of

the maximum particle size. Increasing the particle size resulted in a significant decrease

of E and G (see Figures 4.28a and 4.28b). Considering the porosity results, this reduction

effect was not caused by the pressing process, since there was no influence of the filler

change found. Therefore, this reduction of E and G has to be related to a change in

grain and phase boundaries.

The Poisson’s ratio was influenced by both factors and their interaction, too. Therefore

the means of the Poisson’s ratio are considered (see Figure A.5c in the appendix). It

was found that the maximum particle size effect on Poisson’s ratio clearly influenced the

effect of changing the filler type. Due to this strong interaction, the main effects shown

in Figure A.5c should be ignored. Changing the carbon filler showed either no effect

on Poisson’s ratio for the coarse particle size (3 mm) or an increase for the fine grained

composition. Furthermore, the change of the maximum particle size showed only an

effect with the fine grained carbon filler.

Thus, it can be concluded that the change from a mixture of fine/coarse graphite to a

singular fine graphite resulted in a remarkable decrease of E and G and showed no effect

on the porosity or bulk density. There was no influence on the elastic properties of the

particle size change.


A B AB

effe

ct /

GP

a

−6

−4

−2

02

46


(a) Young’s modulus

A B AB

effe

ct /

GP

a

−3

−2

−1

01

23


(b) Shear modulus

A B AB

effe

ct

−0.

2−

0.1

0.0

0.1

0.2


(c) Poisson’s ratio

Fig. 4.28.: Effect of the carbon filler type (AF) and the maximum particle size (0.045 mm to 3 mm) onthe Young’s and shear modulus and Poisson’s ratio of the reference compositions, the dotted horizontallines represent the confidence levels

Comparison of coarse graphite (NFL) to AF/NFL mix (fine/coarse)

The results for the carbon filler change from ”Mix” to ”NFL” are shown in Figures 4.29

and 4.30. It is apparent that their was no effect of the filler change on the porosity and

bulk density, as observed for the ”Mix” to ”AF” change.

The elastic properties were influenced in the same manner as for the change from mix

to fine. However, the absolute effect values were found to be much smaller than for the

change from ”mix” to ”AF”.

Poisson’s ratio was influenced in the same way as described above. In conclusion, the

change from a mixture of graphite to a coarse graphite affected the elastic properties

less than for the change from a mixture to fine graphite.

Comparison of carbon black (991) to AF/NFL mix (fine/coarse)

The last tested carbon filler type was carbon black. The results of its influence on the

apparent porosity and bulk density are shown in Figure 4.31. Again, the influence of

the filler type was non existent or very low compared to the influence of the maximum

particle size. The porosity was reduced due to the change in the maximum particle size

and furthermore this factor had an increasing effect on the bulk density.

Young’s and shear modulus were mainly affected by the change in maximum particle

size (see Figure 4.32). However, the interaction of both factors was significant, too.

Therefore, the mean values from the appendix will be described here (see Figure A.5).

The effect of the maximum particle size on the elastic properties E and G was influenced


A B AB

effe

ct /

%

−15

−10

−5

05

1015



A B AB

effe

ct /

%

−15

−10

−5

05




A B AB

effe

ct /

g cm

−3

−0.

4−

0.2

0.0

0.2

0.4


(c) Bulk density

Fig. 4.29.: Effect of the carbon filler type (NFL) and the maximum particle size (0.045 mm to 3 mm)on the Apparent porosity and bulk density of the reference compositions, the dotted horizontal linesrepresent the confidence levels

A B AB

effe

ct /

GP

a

−6

−4

−2

02

46



A B AB

effe

ct /

GP

a

−3

−2

−1

01

23


(b) Shear modulus

A B AB

effe

ct

−0.

2−

0.1

0.0

0.1

0.2



Fig. 4.30.: Effect of the carbon filler type (NFL) and the maximum particle size (0.045 mm to 3 mm) onthe Young’s and shear modulus and Poisson’s ratio of the reference compositions, the dotted horizontallines represent the confidence levels


A B AB

effe

ct /

%

−15

−10

−5

05

1015



A B AB

effe

ct /

%

−15

−10

−5

05




A B AB

effe

ct /

g cm

−3

−0.

4−

0.2

0.0

0.2

0.4


(c) Bulk density

Fig. 4.31.: Effect of the carbon filler type (991) and the maximum particle size (0.045 mm to 3 mm)on the Apparent porosity and bulk density of the reference compositions, the dotted horizontal linesrepresent the confidence levels

by the level of the graphite filler type. With carbon black as a filler the effect of the

particle size on E was bigger than for the mix composition. Nevertheless, the Poisson’s

ratio was affected only by the graphite filler type. Changing it to carbon black resulted

in a strong increase of E.

Discussion

The influence of the carbon filler on the elastic properties was found to be less than the

effect of the graphite content. The only significant influence on the elastic properties

was found for the carbon black and fine graphite substitution. The change from a mix of

coarse and fine graphite to coarse graphite on its own showed little to almost no effect.

The decrease of the graphite flake size showed a strong decreasing effect on E and G

but almost no effect on the apparent porosity and bulk density. Thus, the porosity did

not influence these results. The smaller graphite flake size certainly contributed to the

decreasing effect by dispersing energy due to the increase in grain boundaries between

the graphite and alumina particles. Furthermore, the decrease of elasticity could be due

to the increase in the specific surface area of the graphite. The additional surface had to

be wet by the resin binder. Thus less binder certainly will be found between the alumina

and graphite particle which led to a decrease of elasticity.

Other than graphite, carbon black is an amorphous carbon. Therefore its properties are

considerably different to those of graphite [Pierson, 1993a]. Thus, the addition of car-

bon black to the composition considerably changed the nature of elastic response of the


A B AB

effe

ct /

GP

a

−6

−4

−2

02

46



A B AB

effe

ct /

GP

a

−3

−2

−1

01

23


(b) Shear modulus

A B AB

effe

ct

−0.

2−

0.1

0.0

0.1

0.2



Fig. 4.32.: Effect of the carbon filler type (991) and the maximum particle size (0.045 mm to 3 mm) onthe Young’s and shear modulus and Poisson’s ratio of the reference compositions, the dotted horizontallines represent the confidence levels

material. The strong influence of the carbon black addition on Poisson’s ratio illustrates

this very well.

Besides the graphite or carbon filler content, the type of filler also contributed consid-

erably to the elastic properties of carbon-bonded alumina. This should be investigated

deeper, especially the influence on the high temperature behavior.

4.3. Young’s modulus of carbon-bonded open cell foam structures 85

4.3. Young’s modulus of carbon-bonded open cell foam

structures

4.3.1. Room temperature observations

Foam structures are state of the art materials in many industries. The carbon-bonded

open cell foam structures investigated will be used for steel melt filtration. Therefore,

their thermal shock behavior is from a crucial interest to the material engineer. Accord-

ing to the approach of Gibson and Ashby, the so called strut material (bulk material) was

investigated regarding its elastic behavior first. Afterwards, foams of the same composi-

tions were investigated and the results will be compared to findings from the literature.

The influence of the binder content (Carbores®) on the porosity and the elastic moduli

(E and G) was investigated at room temperature. In Figure 4.33a the results are illus-

trated. The porosity clearly was dependent on the Carbores® content after the pressing

as well as after the pyrolysis. With an increase of the Carbores® content the porosity

was linearly reduced. After the pyrolysis this dependence was no longer linear. Still with

an increase of the Carbores® content the porosity was decreased, however stronger at

higher binder amounts.

The Young’s modulus and shear modulus results are shown in Figure 4.33b. Increasing

the Carbores® amount led from 5 to 10 wt % Carbores® to an increase of E and G. At

higher binder contents there was no change of G and a slight increase of E observed.

However, according to a comparison of means of the Carbores® levels (see Table 4.12)

there were only significant differences between the 5 wt % and all other levels. ANOVA

tests were carried out to obtain these influences. The exact result tables can be found

in the appendix A.1.3.

The influence of the apparent porosity of the pyrolyzed material with 20 wt % Carbores®

was investigated to compare the findings with the porosity models proposed by Spriggs

[1961]; Phani and Niyogi [1986]; Nielsen [1984] and Gibson and Ashby [1997]. The

Carbores® content was chosen according to the content of the foam structures. The

results are shown in Figure 4.34. The obtained porosity range by alternating either the

forming technology (pressing or slip casting) or adding a pore forming agent was from

35 to 61 % for the bulk material. Furthermore, results from carbon-bonded foams were

added to extend this range (macroscopic porosity of 85 to 91 %). The measured Young’s

modulus values were in the range of 0.5 to 29 GPa. Within that broad porosity range

all of the models fit the experimental data quite well. However, it was evident that the


Carbores content / %

Por

osity

/ %

5 10 20 30

2025

3035

4045

50 pressedpyrolyzed


Carbores content / %

Youn

g's

and

shea

r m

odul

us /

GP

a

5 10 20 30

510

1520

2530

Young's modulusShear modulus

(b) Shear modulus

Fig. 4.33.: Influence of the Carbores® content on the apparent porosity after the pressing / pyrolysis, onthe Young’s and shear modulus of a filter bulk material

Tab. 4.12.: Results of the Tukey range test with a p-value of 0.05 for the different Carbores® contentsand response values (E, G); the values tested were evaluated at room temperature, p < 0.05 indicatessignificant differences between the tested pair

Carbores® pairs pE pG10− 5 0.0000805 0.000011120− 5 0.0000016 0.000007030− 5 0.0000001 0.000013420− 10 0.7236276 0.999999130− 10 0.2187615 0.997944230− 20 0.7860770 0.9972654


●

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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

010

2030

40

Pore volume fraction

E /

GP

a

SpriggsPhani et al.NielsenGibson et al.

Fig. 4.34.: Young’s modulus of the bulk and foam material (20 wt % Carbores® content) in dependenceon the porosity; Models found in the literature were fitted against the experimental data to analyze theirapplicability for this composite material

Tab. 4.13.: Estimates of the model fits on the experimental data of E(P ) for the carbon-bonded bulkand foam material (20 wt % Carbores® content), p < 0.05 indicates significance of the estimates

Model E0 / GPa p Estimate 2 p

Spriggs [1961] 176.32 < 2e− 16 5.62 < 2e− 16Nielsen [1984] 283.91 0.0519 0.08 0.08Phani and Niyogi [1986] 84.84 < 2e− 16 2.93 < 2e− 16Gibson and Ashby [1997] 73.51 < 2e− 16 3.06 < 2e− 16

Spriggs model did not fit the highest porosity well. The reason therefore was explained

in the chapter ”State of the art”. This model does not fulfill the boarder condition

p = 0 −→ E = 0. On the other hand did the Gibson and Ashby model not fit the lower

porosity data well, which was not surprising since it was proposed for cellular materials.

Furthermore, the estimates of the model fits (see Table 4.13) were quite different. The

Nielsen and Spriggs model returned very high E0 values whereas the Gibson and Ashby

and Phani and Niyogi model returned significant lower values. The significance of these

estimates was below 0.05 for all models except for Nielsen’s model.

4.3.2. High temperature observations

The high temperature measurements were carried out only for the 20 wt % Carbores®

content bulk samples, because this was the used amount for the foam structures as well.


Tab. 4.14.: Absolute Young’s modulus values of the bulk material and the filter structure before thehigh temperature measurement (pyrolyzed at 800 ◦C)

Material E / GPa

Bulk ≈ 20.0Foam ≈ 0.5

The initial values of E are shown in Table 4.14. The Young’s modulus of the foam

structure should only be regarded as an approximate value since the equations for the

calculation of E only are valid for homogeneous, isotropic materials. In Figure 4.35a the

Young’s modulus (normalized to the initial room temperature value) in dependence on

the temperature is shown. Two measurement sets were carried out; one up to 1000 ◦C

and the second up to 1450 ◦C. Two samples each set were investigated. The filter struc-

ture was also measured up to 1000 ◦C and only one sample was observed. The max-

imum temperature of 1000 ◦C was defined due to an increasing oxidation and further

microstructural changes above this temperature which would disturb the analysis of the

measurement especially of the filter structures.

The change of E for the bulk material is quite comparable to the evolution of E of the

reference and industry related compositions discussed above. There was a slight decrease

of E up to 500 ◦C. Above E increase up to the samples former pyrolysis temperature

which was in this case 800◦C. Above 800◦C a small decrease was registered which was

superimposed for the 1000◦C measurement by an increase of E during the holding time.

After holding at 1000 ◦C E remained almost constant 5 % above the initial value. In-

creasing the temperature above 1000 ◦C resulted in a strong decrease of E (-10 %) up

to 1450 ◦C. In Figure 4.35c E(T ) of alumina is shown, to compare that decrease of the

carbon-bonded alumina with the one obtained for pure alumina above 1200 ◦C.

During the holding time at 1450 ◦C E of the carbon-bonded alumina increased signifi-

cantly, as seen also in the sections above. After the holding time there was an increase of

E up to approximately 1000 ◦C. Below E remained constant at around 5 % of the initial

value.

The values obtained for the filter structure were very strong scattered. Especially during

holding a strong scattering could be observed. The trend of E(T ) however was compara-

ble to that of the bulk samples. A decrease of E during heating up to 500 ◦C, followed by

an increase up to the former pyrolysis and a small decrease up to 1000 ◦C. Nevertheless,

during cooling E decreased instead of remaining constant. Thus, the residual E was

around 15 % below the initial value.

Several problems came up during this experiment. Besides the mentioned oxygen attack


0 500 1000 1500

−15

−10

−5

05

10

Temperature / °C

(E−

E0)

E0

/ %

0 500 1000 1500

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1000 °C Bulk1450 °C Bulk1000 °C Filter


0 500 1000 1500

−3

−2

−1

01

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(l−

l 0)

l 0 /

%

0 500 1000 1500

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10 %20 %

(b) Thermal expansion measurement

0 500 1000 1500

−25

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E0)

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/ %

0 500 1000 1500

− 8 %

(c) HT E of alumina

Fig. 4.35.: Influence of the temperature on the Young’s modulus and linear change of the bulk materialand filter structures which were pyrolyzed at 800 ◦C; the Young’s modulus dependent on the temperatureof alumina is shown at the bottom for a comparison of the nonlinear decrease of E above 1200 ◦C of thealumina and the carbon-bonded alumina


due to residual oxygen within the furnace, the area of excitation of the filter was not

even. Thus, the impact energy was not equal each time. Furthermore, it is not assured

that a rectangular foam structure vibrates in the same way as a dense rectangular bar

does. Additionally, the measurement of the foam dimensions added uncertainty.

Thermal expansion measurements were carried out for a 20 wt % and a 10 wt % Carbores®

bulk material sample. The lower amount of binder was investigated to obtain the con-

tribution of the binder on the thermal expansion of this composite material (see Figure

4.35b).

Both compositions showed a similar almost linear expansion behavior up to the former

pyrolysis temperature (0.3 − 0.4 %). Above, the expansion turned into a shrinkage and

the intensity of shrinkage was dependent on the Carbores® content because the 20 wt %

sample shrunk 1.5 % up to 1450 ◦C while the shrinkage was only 0.24 % for the 10 wt %

composition. The cooling behavior was similar again for both compositions. A linear

decrease with the same slope.

4.3.3. Discussion

The influence of the Carbores® content on the elasticity of the bulk material at room

temperature is important for the filter design and probable finite element computa-

tion. To exclude an influence of the Carbores® content on the porosity of the samples,

their apparent porosity after the pressing was investigated. A clear linear decrease of

the porosity with increasing Carbores® content revealed its significant influence on the

pressing behavior. The Carbores® improved the compaction of the material either by

optimizing the particle size distribution (filling the space particles) or by acting as a

lubricant during pressing. Likely, both mechanism contributed to this result.

The results revealed a slight increase of E with increasing the binder content. However,

the lower porosity of the higher Carbores® containing compositions contributed cer-

tainly to this effect. Therefore, it can be concluded that an increase of E was not only

affected by an increase of the binder but also by an enhancement of the compaction pro-

cess due to the higher binder amount. Klemm et al. [2013] found a relationship between

the cold modulus of rupture (CMOR) and the Carbores® content. With increasing

binder content CMOR increased, too. The same conclusion was found by Soltysiak et al.

[2013] for the effective strength evaluated by means of a small punch test. These results

are quite contrary to the Young’s modulus results in dependence on the binder content.

However, the material investigated in those studies contained additional graphite and


carbon black. Furthermore, no porosity results were reported by Soltysiak et al. which

complicates a comparison. Nevertheless, an increase of the strength of this material could

be possible even without an increase of E. Since the bonding phase (coke like structure)

was still the same, its stiffness has not to be changed by increasing its amount. But

the strength could be improved due to a higher amount of bonds between the composite

constituents.

The porosity dependence of the 20 wt % Carbores® bulk material and foam structure

followed the assumed exponential like relationship. The different models fitted the ex-

perimental data in a very broad porosity range. As already explained in the literature,

the model by Spriggs [1961] did not fit the data as well as the others. Furthermore, the

estimates of the model by Nielsen [1984] were not significant. Therefore, both models

might not be suitable for a prediction of E within the investigated porosity range. The

models by Gibson and Ashby [1997] and Phani and Niyogi [1986] fitted the data quite

well. Furthermore, the estimation of E0, the Young’s modulus of the pore free material,

was quite in the same range (73 and 84 GPa). Therefore, these two models might be

appropriate for E prediction within the investigated temperature range of this material.

Furthermore, the power factor n of the Gibson and Ashby model was computed and

found to be approximately 3. This parameter describes the cell structure of the foam

and was found to be 2 for open cell foams. The constant C1 was assumed to be 1 ac-

cording to Gibson and Ashby [1997].

These results could be used for the design of foam structures or thermal shock prediction

within the observed porosity range. A big drawback is still the uncertainty of E0 and the

problem of forming samples with different porosity without influencing the microstruc-

ture (for example due to organic pore forming agents). Further investigations should be

made to clear this up.

The high temperature Young’s modulus of the bulk material of the filter coating was

found to be in accordance to the model introduced earlier (see section 4.1). A small

decrease of E up to 500 ◦C was followed by an increase up to the former pyrolysis tem-

perature. However, compared to the amount of E increase of the reference and industry

compositions (70 to 150 %) the change of E for the bulk material was very small (2 %).

Still it seems like some preexisting gaps or pores were closed up to the former pyrolysis

temperature. A big difference between those earlier compositions and the bulk compo-

sition (AC4) was the maximum alumina particle size of ≈ 3µm compared to 0.045 mm

(the lowest maximum particle size of the reference compositions). This result confirms

the theory of gap closing during reheating. Smaller particles retain smaller gaps and

therefore lead to less E increase during reheating.


Above that, the behavior of the bulk and filter material differed significantly from that of

the earlier compositions. E decreased very strong above 1000 ◦C up to 1450 ◦C. During

cooling E increased in the same way as it decreased during heating. From about 1000 ◦C

down to room temperature E remained constant. This cooling behavior was completely

similar to that of common oxides like alumina or magnesia [Wachtman and Lam, 1959].

The nonlinear decrease above the former pyrolysis temperature might be induced due to

two different mechanisms. Wachtman and Lam [1959] observed such a phenomena for

polycrystalline alumina and attributed it to a ”viscous slip of grain boundaries”. Com-

paring E(T ) of alumina and the carbon-bonded bulk material shows a similar decrease

of approximately 8 % down to 1400 ◦C. The second possible effect contributing to this

nonlinear decrease would be a further transformation of the Carbores®. According to

Dopita et al. [2014] in the temperature range of 800 to 1400 ◦C a significant increase of

atoms within one graphitic layer (retained from the Carbores®), as well as an increase

of these layers was observed. This on the other hand could be interpreted as a kind

of densification since atoms were more ordered than before. Thus, a densification of

one constituent could also lead to higher porosity inside a composite due to a volume

shrinkage. These two mechanisms are likely to be the main reasons for the nonlinear

decrease of E above the former pyrolysis temperature. Furthermore, the influence of the

Carbores® on E was illustrated by the 1000 ◦C measurement of the bulk material. There

was a similar increase of E after the measurement as for the 1450 ◦C cycle. This could be

probably affected due to a further transformation of the Carbores® during the holding

time. The thermal expansion measurement underlined the influence of the Carbores®.

Above the former pyrolysis temperature the material started shrinking which was much

stronger for the high Carbores® containing sample (20 wt %). This shrinkage might be a

sign of densification either of the Carbores® or the alumina. Certainly this fine alumina

could sinter already above 1000 ◦C. Therefore, it can not be determined exactly which

phase densified.

The relative Young’s modulus of the foam structure followed the same trend as the bulk

material. This result is in accordance with the findings of Gibson and Ashby. They

described E as a function of the bulk or strut material. Furthermore, they included the

well known E(T ) equation by Wachtman et al. [1961] into their model, a linear depen-

dence of E on T . However, due to the composite character of the strut material, which

was described and explained earlier, such a linear dependence of E on T for the foam

structure investigated in this study was not found. The difference between the bulk

material and the filter structure during cooling might be caused by a slight oxidation

attack, which could be much stronger for the foam structure since the attack-able surface


is much higher than that of the bulk material. Furthermore, the result revealed a strong

scattering of the data since the response signal of the foam structure was damped very

strong and the impulse area was quite uneven. Nevertheless, the measurement revealed

clearly a link between bulk and foam material.

95

5. Experimental errors and error analysis

Generally, there are two different kinds of errors to distinguish. Systematic and random

errors. Systematic errors often appear due to a wrong measurement setup for example

using a not calibrated caliper (i.e. +1 mm). This means every measurement will be

1 mm above the true value. Often this is described as the accuracy of an experiment. It

is not possible to increase the accuracy by a bigger amount of samples.

Random errors represent the uncertainty of an experiment and are often referred to in

terms of precision. For example setting up an experiment with always the same initial

conditions may be impossible (i.e. exact sample dimensions). Random errors can be

calculated and mathematically expressed by a standard deviation or confidence interval

of 95 %. In this case the presented values of a variable represent estimates. These

estimates are equal to the true value with a certain probability (95 % for a confidence

interval with p < 0.05).

In case of this study the main experiment carried out was the measurement of Young’s

modulus, shear modulus and Poisson’s ratio. Systematic errors arising from this exper-

iment could be:

• a wrong support distance which would affect the damping behavior

• a flawed thermocouple resulting in an erroneous temperature measurement

• residual oxygen within the furnace during the measurement under argon atmo-

sphere

The last systematic error definitely was evident during the experiments of this study.

The mass of the samples was measured before and after a measurement. Therefore, a

mass loss could be connected to an oxidation caused by that residual oxygen. However, it

was found that even a very small oxidation did affect the result of the high temperature

measurement in a significant way.

Classical random errors like the measurement of the specimen dimensions and mass

certainly contributed to the results presented above. At room temperature these errors

96 5. Experimental errors and error analysis

were taken into account due to the presentation of a mean value and a confidence interval

for this value. Furthermore, many of the room temperature measurements were planned

and carried out using design of experiments and the analysis formulas according to

Montgomery [2001]. Within the presented effect diagrams a confidence interval was

presented taking random errors into account. Furthermore, these effects were calculated

using an effect matrix according to the principles of the design of experiments. Due to

addition and subtraction with different algebraic pre signs a systematic error would be

automatically eliminated. The introduced effect of residual oxygen within the furnace

was a source of random errors, too. Even though the atmosphere provided within the

furnace was always the same, due to the application of the same evacuation and purge

cycles for all measurements, the samples differed. For example samples without graphite

only contained a carbonaceous, amorphous carbon phase which was more prone for

oxidation than graphite. Therefore, the same amount of oxygen affected the samples in

a different way. This effect only could be suppressed by using an oxygen free atmosphere

which is almost impossible using a furnace with highly porous lining material.

97

6. Summary and outlook

Thermal shock resistance is a key property of refractory materials. Its determination and

prediction is essential for the design of structural refractories as well as lining materials.

Young’s modulus of elasticity is a crucial parameter for the calculation of thermal shock

resistance. Providing information regarding high temperature elasticity could promote

the design of new refractories.

In this study the elasticity of carbon bonded refractories was investigated. At first a

series of industry related compositions was investigated to obtain an overview of the

general high temperature elasticity of this material class. It was found that the pyrol-

ysis temperature of these materials determined the Young’s modulus. During reheating

Young’s modulus always increased up to the former pyrolysis temperature independently

of the composition and porosity. Furthermore, at the maximum temperature of 1450◦C

an increase of E, attributed to sintering, was observed. Also characteristic for carbon-

bonded materials was a hysteresis during cooling. After one measurement the residual

Young’s modulus was mostly lower than the initial one. A similar behavior was also

found for the additionally carried out thermal expansion measurements. Below the for-

mer pyrolysis temperature the coefficient of thermal expansion (CTE) was lower than

that above this temperature. This typical behavior was more or less found for all com-

positions and technological treatments.

A model was described based on literature findings and supported by the carried out ex-

periments. Basically the behavior described above was a result of the composite nature

of carbon bonded materials comprised from alumina, amorphous carbon and graphite.

The coarse alumina and graphite particles are embedded in a matrix of fine alumina and

amorphous carbon. Due to the CTE mismatch of these constituents, gaps were assumed

around the coarse particles. These gaps formed during cooling after the pyrolysis since

the alumina as well as the graphite were assumed to contract faster than the surround-

ing matrix. After reheating (during the E(T )-measurement) the constituents expanded

again. Near the former pyrolysis temperature the former gaps were closed bit by bit.

98 6. Summary and outlook

Due to this closure the Young’s modulus increased and also the expansion of the macro-

scopic sample increased because now the stronger expanding constituents contributed to

the measured expansion behavior. It has to be emphasized that the porosity of the com-

posite is assumed to remain open. The gaps between two materials (matrix/alumina)

are assumed to be closed.

Besides this similar behavior significant influences of the composition and porosity on

the Young’s modulus were obtained. The type of binder (resin or modified pitch tar) did

not influence the high temperature elasticity significantly, whereas the amount of binder

affected that behavior remarkably. Increasing the binder content resulted in a decrease

of the maximum E and lower residual E values after a measurement. The higher binder

amount contributed to a lower volume fraction of coarse particles which affected the

amount of gaps introduced in the matrix. Thus, less gaps were closed during reheating

resulting in a lower E increase. Furthermore, the higher amount of amorphous carbon

contributed to a lower overall expansion correlating with the E(T ) measurement.

The influence of the graphite amount and maximum alumina particle size on the elasticity

was investigated at room and high temperature. It was found that both factors interact

with each other. Thus, the main effects were dependent on the level of the second factor.

The obtained results were compared to calculated Hashin and Shtrikman [1963] (HS)

bounds. There was a big discrepancy between the calculated and measured values due

to the heterogeneous nature of the material. The decreasing tendency of E was not

represented in the direct measured values. However, the porosity contributed to these

results whereas the HS-bounds did not take the porosity into account. Furthermore, the

parameter b of the E(P ) model of Spriggs [1961] was calculated using the lower HS-

bound and the experimental data. This parameter showed a clear dependence on the

maximum alumina particle size but almost not on the graphite content. Therefore, it

is assumed that the pore shape contributed to this result because different particle size

distributions cause different pore shapes. Furthermore, other models from the literature

already showed the pore shape influence. This is a possible task for future work to obtain

the exact influence of the pore shape on the Young’s modulus of carbon-bonded alumina.

The influence of the carbon amount and maximum particle size on the high temperature

Young’s modulus was not consistent as already observed at room temperature. The

effect of the graphite content on E(T ) was dependent on the maximum particle size.

Nevertheless, the maximum particle size had a global effect on E(T ). The overall increase

of E during heating was lowest for the smallest particle size. In terms of thermal shock

resistance it could be concluded that a lower elasticity during reheating might improve

the thermal shock resistance. However, the initial values of E have to be considered

99

since the discussed Young’s modulus evolution was always relative. Therefore, a global

statement was not possible regarding the influence of both factors on the thermal shock

resistance. Furthermore, the elasticity is just one part contributing to the thermal shock

behavior.

In addition to the composition influence on the elastic behavior the contribution of differ-

ent porosities was investigated, too. At room temperature, models found in the literature

were applied to the experimental data. The fits of these models were satisfactory within

the investigated porosity range (14 − 21 % and 35 − 95 %). Outside the investigated

range the models differed remarkably. Furthermore, it was found that there is no model

which describes the porosity of carbon bonded compositions within a porosity range of

0 to 90 % accurately. However, this was also found for oxide materials. Therefore, the

appropriate model for the investigated porosity range has to be chosen carefully.

At high temperatures, the behavior described above was found for all porosities. The

curves only differed quantitatively since the initial E values differed in dependence on

the porosity. Thus, the porosity did not significantly influence the high temperature

elasticity of the investigated materials.

Finally, the portability of the results obtained for coarse particle carbon-bonded refrac-

tories to fine grained bulk material and filter structures was investigated. The evolution

of E(T ) of the bulk material as well as of the filter structures was comparable to the

coarse particle samples. However, the overall change of E(T ) was in the range of ±10 %

which was very low compared to the coarse compositions (at least ±50 %). Compared

to that compositions, this material might be regarded as more stable in terms of ther-

mal shock resistance, however again the initial elasticity was quite high compared to

the coarse samples. Furthermore, the measurement of a foam structure was successfully

carried out. However, several problems occurred with that measurement questioning the

results obtained for the foam structures. These problems should be addressed in further

research projects.

These findings support the understanding of the microstructure evolution of carbon-

bonded alumina in the temperature range of 25 − 1450◦C. Furthermore, they might

prepare the ground for further research connecting the high temperature Young’s mod-

ulus measurement with the modeling of thermal shock resistance.

101

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A. Appendix

A.1. Additional results

Complete confidential plots and ANOVA tables can be found within this section.

A.1.1. Influence of graphite content and maximum particle size

Room temperature results


Por

osity

afte

r pr

essi

ng /

%

0 10 20 30

05

1015

2025


0.045 mm1 mm3 mm

(a) Porosity after pressing


App

aren

t por

osity

afte

r py

roly

sis

/ %

0 10 20 30

010

2030

40

max. particle size

0.045 mm 1 mm 3 mm

(b) Apparent porosity


Bul

k D

ensi

ty /

g cm

−3

0 10 20 30

2.0

2.2

2.4

2.6

2.8

max. particle size

0.045 mm 1 mm 3 mm

(c) Bulk density

Fig. A.1.: Effect of the graphite content and maximum particle size on the porosity after pressing,apparent porosity and bulk density after pyrolysis at room temperature

Tab. A.1.: ANOVA statistic for the factors graphite content and maximum particle size on the porosityafter pressing (PP) and after the pyrolysis (AP), as well as for the bulk density (BD)

Response PP AP BDFactor p-value p-value p-value

Graphite amount < 2e− 16 < 2e− 16 < 2e− 16max. particle size < 2e− 16 < 2e− 16 < 2e− 16Interaction of both < 2e− 16 < 2e− 16 < 2e− 16

114 A. Appendix


Youn

g's

mod

ulus

/ G

Pa

0 10 20 30

510


0.045 mm1 mm3 mm



She

ar m

odul

us /

GP

a

0 10 20 30

24

68


0.045 mm1 mm3 mm

(b) Shear modulus


Poi

sson

's r

atio

0 10 20 30

0.05

0.10

0.15

0.20

0.25

0.30 max. particle size

0.045 mm1 mm3 mm


Fig. A.2.: Effect of the graphite content and maximum particle size on the Young’s modulus, shearmodulus and Poisson’s ratio at room temperature


Dam

ping

0 10 20 30

0.00

00.

004

0.00

80.

012

max. particle size

0.045 mm 1 mm 3 mm

(a) Damping


(l−

l 0)

l 0 /

%

0 10 20 30

−0.

8−

0.6

−0.

4−

0.2

0.0

max. particle size

0.045 mm1 mm3 mm

(b) l − l0/l0

Fig. A.3.: Effect of the graphite content and maximum particle size on the damping behavior and changein length of the sample at room temperature

Tab. A.2.: ANOVA summary of the Young’s modulus in dependence on the factors A - graphite contentand B - maximum particle size as well as on their interaction

Df Sum Sq Mean Sq F value Pr(>F)

A 3 82.8 27.62 18.41 1.02e-09 ***

B 2 469.5 234.75 156.50 < 2e-16 ***

A:B 6 591.1 98.52 65.68 < 2e-16 ***

Residuals 108 162.0 1.50

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

A.1. Additional results 115

Tab. A.3.: ANOVA summary of the shear modulus in dependence on the factors A - graphite contentand B - maximum particle size as well as on their interaction


A 3 33.92 11.31 31.01 1.54e-14 ***

B 2 101.10 50.55 138.61 < 2e-16 ***

A:B 6 125.91 20.99 57.54 < 2e-16 ***

Residuals 108 39.39 0.36

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.4.: ANOVA summary of the Poisson’s ratio in dependence on the factors A - graphite contentand B - maximum particle size as well as on their interaction


A 3 0.3586 0.11953 103.435 < 2e-16 ***

B 2 0.0433 0.02167 18.751 1.02e-07 ***

A:B 6 0.0360 0.00599 5.188 0.000101 ***

Residuals 108 0.1248 0.00116

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.5.: ANOVA summary of the damping in dependence on the factors A - graphite content and B -maximum particle size as well as on their interaction


A 3 1.317e-04 4.389e-05 30.679 2.17e-14 ***

B 2 1.106e-04 5.528e-05 38.641 2.34e-13 ***

A:B 6 3.759e-05 6.270e-06 4.379 0.000539 ***

Residuals 107 1.531e-04 1.430e-06

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

1 observation deleted due to missingness

116 A. Appendix

Tab. A.6.: ANOVA summary of the apparent porosity in dependence on the factors A - graphite contentand B - maximum particle size as well as on their interaction


A 3 1691 563.7 5187.3 <2e-16 ***

B 2 5526 2763.2 25429.7 <2e-16 ***

A:B 6 68 11.3 103.6 <2e-16 ***

Residuals 108 12 0.1

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.7.: ANOVA summary of the bulk density in dependence on the factors A - graphite content andB - maximum particle size as well as on their interaction


A 3 0.541 0.1803 1453.1 <2e-16 ***

B 2 4.078 2.0388 16432.5 <2e-16 ***

A:B 6 0.108 0.0179 144.5 <2e-16 ***

Residuals 108 0.013 0.0001

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.8.: ANOVA summary of the porosity after pressing in dependence on the factors A - graphitecontent and B - maximum particle size as well as on their interaction


A 3 964 321.2 399.98 <2e-16 ***

B 2 4825 2412.7 3004.72 <2e-16 ***

A:B 6 121 20.1 25.09 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



Tab. A.9.: ANOVA summary of the linear change in length of the samples after the pyrolysis in depen-dence on the factors A - graphite content and B - maximum particle size as well as on their interaction


A 3 0.4450 0.1483 27.505 3.31e-13 ***

B 2 1.8870 0.9435 174.949 < 2e-16 ***

A:B 6 0.1667 0.0278 5.151 0.000112 ***

Residuals 105 0.5663 0.0054

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3 observations deleted due to missingness

118 A. Appendix

Tab. A.10.: ANOVA summary of the Young’s modulus from room temperature to 1450◦C of the 0.045 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C

Df Sum Sq Mean Sq

B 2 837.9 418.9

Error: Within


B 3 20160 6720 329.32 <2e-16 ***

D 29 227323 7839 384.15 <2e-16 ***

B:D 87 35229 405 19.84 <2e-16 ***

Residuals 232 4734 20

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

High temperature measurement results


Tab. A.11.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the temperature influence on E for the 0.045 mm compositions at heating; foreach pair a p-value is shown, p < 0.05 indicates a significant difference

Pairwise comparisons using paired t tests

data: joern.up.0.045$E and joern.up.0.045$B

0 10 20

10 7.3e-08 - -

20 1.6e-10 0.057 -

30 1.1e-09 0.014 3.0e-07

P value adjustment method: holm

Tab. A.12.: ANOVA summary of the Young’s modulus from 1450◦C to room temperature of the 0.045 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C

Df Sum Sq Mean Sq

B 2 1596 798.2

Error: Within


B 3 190678 63559 468.564 < 2e-16 ***

D 29 372837 12856 94.778 < 2e-16 ***

B:D 87 23982 276 2.032 2.53e-05 ***

Residuals 196 26587 136

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

120 A. Appendix

Tab. A.13.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the temperature influence on E for the 0.045 mm compositions at cooling; foreach pair a p-value is shown, p < 0.05 indicates a significant difference


data: joern.down.0.045$E and joern.down.0.045$B

0 10 20

10 < 2e-16 - -

20 < 2e-16 0.00035 -

30 < 2e-16 0.00045 4.5e-13


Tab. A.14.: ANOVA summary of the Young’s modulus during the soak time of the 0.045 mm compositionsin dependence on the factors B - graphite content and D - time as well as on their interaction

Error: C


Residuals 2 89.7 44.85

Error: Within


B 3 93.9 31.29 2.182 0.0953 .

D 11 1476.4 134.22 9.359 3.87e-11 ***

B:D 33 100.1 3.03 0.212 1.0000

Residuals 94 1348.0 14.34

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.15.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the graphite content influence on the soak time behavior of E for the 0.045 mmcompositions; for each pair a p-value is shown, p < 0.05 indicates a significant difference


data: soak.0.045$E and soak.0.045$B

0 10 20

10 0.011 - -

20 1.000 0.145 -

30 1.000 0.027 1.000


Tab. A.16.: ANOVA summary of the Young’s modulus from room temperature to 1450◦C of the 3 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C


B 1 19.31 19.31 0.27 0.695

Residuals 1 71.61 71.61

Error: Within


B 3 55343 18448 1345.68 <2e-16 ***

D 29 1445427 49842 3635.82 <2e-16 ***

B:D 87 33355 383 27.97 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

122 A. Appendix

Tab. A.17.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the temperature influence on E for the 3 mm compositions at heating; for eachpair a p-value is shown, p < 0.05 indicates a significant difference


data: joern.up.3$E and joern.up.3$B

0 10 20

10 < 2e-16 - -

20 < 2e-16 5.2e-05 -

30 < 2e-16 < 2e-16 1.9e-14


Tab. A.18.: ANOVA summary of the Young’s modulus from 1450◦C to room temperature of the 3 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C


B 1 596.9 596.9 0.835 0.529

Residuals 1 715.1 715.1

Error: Within


B 3 10223 3408 37.28 <2e-16 ***

D 29 1286356 44357 485.22 <2e-16 ***

B:D 87 63944 735 8.04 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.19.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the temperature influence on E for the 3 mm compositions at cooling; for eachpair a p-value is shown, p < 0.05 indicates a significant difference


data: joern.down.3$E and joern.down.3$B

0 10 20

10 0.0054 - -

20 0.1284 9.2e-05 -

30 0.8996 0.0034 0.0114


Tab. A.20.: ANOVA summary of the Young’s modulus during the soak time of the 3 mm compositionsin dependence on the factors B - graphite content and D - time as well as on their interaction

Error: C

Df Sum Sq Mean Sq

B 1 33.27 33.27

Error: Within


B 3 540.2 180.07 186.479 < 2e-16 ***

D 11 8.9 0.81 0.841 0.602

B:D 33 106.6 3.23 3.345 9.86e-05 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

124 A. Appendix

Tab. A.21.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the graphite content influence on the soak time behavior of E for the 3 mmcompositions; for each pair a p-value is shown, p < 0.05 indicates a significant difference


data: soak.3$E and soak.3$B

0 10 20

10 8.2e-08 - -

20 3.0e-10 1.9e-09 -

30 5.4e-08 1.2e-05 1.2e-05


Tab. A.22.: ANOVA summary of the Young’s modulus from room temperature to 1450◦C of the 1 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C



Error: Within


B 3 34661 11554 914.47 <2e-16 ***

D 29 1064931 36722 2906.49 <2e-16 ***

B:D 87 35455 408 32.26 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.23.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the temperature influence on E for the 1 mm compositions at heating; for eachpair a p-value is shown, p < 0.05 indicates a significant difference


data: joern.up.1$E and joern.up.1$B

0 10 20

10 3.8e-16 - -

20 1.2e-09 0.00029 -

30 4.1e-14 4.9e-11 < 2e-16


Tab. A.24.: ANOVA summary of the Young’s modulus from 1450◦C to room temperature of the 1 mmcompositions in dependence on the factors B - graphite content and D - temperature as well as on theirinteraction

Error: C

Df Sum Sq Mean Sq

B 2 13730 6865

Error: Within


B 3 36919 12306 73.754 <2e-16 ***

D 29 807772 27854 166.934 <2e-16 ***

B:D 87 104879 1206 7.225 <2e-16 ***

Residuals 177 29534 167

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

126 A. Appendix

Tab. A.25.: ANOVA summary of the Young’s modulus during the soak time of the 1 mm compositionsin dependence on the factors B - graphite content and D - time as well as on their interaction

Error: C


Residuals 1 15.45 15.45

Error: Within


B 3 65.96 21.985 9.338 0.000211 ***

D 6 29.58 4.930 2.094 0.087206 .

B:D 18 27.82 1.545 0.656 0.821742

Residuals 27 63.57 2.354

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.26.: Results of the pairwise Student’s t-test (adjusted p-value according to the Holm-Bonferronimethod [Holm, 1979]) of the graphite content influence on the soak time behavior of E for the 1 mmcompositions; for each pair a p-value is shown, p < 0.05 indicates a significant difference


data: soak.1$E and soak.1$B

0 10 20

10 0.1813 - -

20 0.0205 9.4e-05 -

30 0.0205 0.0049 0.1813



Tab. A.27.: ANOVA summary of the Young’s modulus in dependence on the factors A - particle sizeand B - graphite content as well as on their interaction after the high temperature measurement


A 2 15403 7701 142.007 5.01e-14 ***

B 3 5168 1723 31.763 1.60e-08 ***

A:B 6 1183 197 3.634 0.0104 *


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.28.: ANOVA summary of the mass loss in dependence on the factors A - particle size and B -graphite content as well as on their interaction after the high temperature measurement


A 2 1.2129 0.6064 19.364 9.84e-06 ***

B 3 0.4258 0.1419 4.532 0.0118 *

A:B 6 0.5951 0.0992 3.167 0.0197 *

Residuals 24 0.7516 0.0313

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

128 A. Appendix

Tab. A.29.: ANOVA summary of the porosity change in dependence on the factors A - particle size andB - graphite content as well as on their interaction after the high temperature measurement



A 2 5.913 2.9565 18.254 1.52e-05 ***

B 3 4.641 1.5470 9.552 0.000246 ***

A:B 6 2.854 0.4756 2.937 0.027120 *

Residuals 24 3.887 0.1620

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


A.1.2. Influence of carbon filler type and maximum particle size

Carbon filler type

Por

osity

afte

r pr

essi

ng /

%

AF CB Mix NFL

05

1015

2025


0.045 mm1 mm3 mm

(a) Porosity after pressing

Carbon filler type

App

aren

t por

osity

afte

r py

roly

sis

/ %

AF CB Mix NFL

1015

2025

3035

max. particle size

0.045 mm 1 mm 3 mm

(b) Apparent porosity

Carbon filler type

Bul

k D

ensi

ty /

g cm

−3

AF CB Mix NFL

2.2

2.4

2.6

2.8

max. particle size

0.045 mm 1 mm 3 mm

(c) Bulk density

Fig. A.4.: Effect of the carbon filler type and maximum particle size on the porosity after pressing,apparent porosity and bulk density after pyrolysis at room temperature

Carbon filler type

Youn

g's

mod

ulus

/ G

Pa

AF CB Mix NFL

68

1012

1416

max. particle size

0.045 mm 1 mm 3 mm


Carbon filler type

She

ar m

odul

us /

GP

a

AF CB Mix NFL

23

45

67


0.045 mm 1 mm 3 mm

(b) Shear modulus

Carbon filler type

Poi

sson

's r

atio

AF CB Mix NFL

0.0

0.1

0.2

0.3

0.4

0.5

max. particle size

0.045 mm 1 mm 3 mm


Fig. A.5.: Effect of the carbon filler type and maximum particle size on the Young’s modulus, shearmodulus and Poisson’s ratio at room temperature

130 A. Appendix

Carbon filler type

Dam

ping

AF CB Mix NFL0.

000

0.00

50.

010

0.01

50.

020

max. particle size

0.045 mm 1 mm 3 mm

(a) Damping

Carbon filler type

(l−

l 0)

l 0 /

%

AF CB Mix NFL

−0.

8−

0.6

−0.

4−

0.2

0.0

max. particle size

0.045 mm1 mm3 mm3

(b) l − l0/l0

Fig. A.6.: Effect of the carbon filler type and maximum particle size on the damping behavior and changein length of the sample at room temperature

Tab. A.30.: ANOVA summary of the Young’s modulus in dependence on the factors A - carbon fillertype and B - maximum particle size as well as on their interaction


A 3 324.6 108.21 88.74 < 2e-16 ***

B 2 153.2 76.58 62.80 < 2e-16 ***

A:B 6 123.4 20.56 16.86 1.39e-13 ***

Residuals 106 129.3 1.22

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.31.: ANOVA summary of the shear modulus in dependence on the factors A - carbon filler typeand B - maximum particle size as well as on their interaction


A 3 61.86 20.619 103.11 < 2e-16 ***

B 2 6.69 3.347 16.74 4.81e-07 ***

A:B 6 36.98 6.163 30.82 < 2e-16 ***

Residuals 106 21.20 0.200

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



Tab. A.32.: ANOVA summary of the Poisson’s ratio in dependence on the factors A - carbon filler typeand B - maximum particle size as well as on their interaction


A 3 0.2815 0.09384 78.66 <2e-16 ***

B 2 0.5780 0.28900 242.26 <2e-16 ***

A:B 6 0.4680 0.07800 65.38 <2e-16 ***

Residuals 106 0.1265 0.00119

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.33.: ANOVA summary of the damping in dependence on the factors A - carbon filler type andB - maximum particle size as well as on their interaction


A 3 0.0002343 7.811e-05 18.80 7.47e-10 ***

B 2 0.0005397 2.699e-04 64.97 < 2e-16 ***

A:B 6 0.0003330 5.549e-05 13.36 3.15e-11 ***

Residuals 106 0.0004403 4.150e-06

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.34.: ANOVA summary of the apparent porosity in dependence on the factors A - carbon fillertype and B - maximum particle size as well as on their interaction


A 3 54 17.9 115.72 <2e-16 ***

B 2 5690 2845.0 18417.76 <2e-16 ***

A:B 6 65 10.9 70.25 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

132 A. Appendix

Tab. A.35.: ANOVA summary of the bulk density in dependence on the factors A - carbon filler typeand B - maximum particle size as well as on their interaction


A 3 0.049 0.0162 136.4 <2e-16 ***

B 2 4.522 2.2608 18977.7 <2e-16 ***

A:B 6 0.074 0.0124 103.7 <2e-16 ***

Residuals 108 0.013 0.0001

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.36.: ANOVA summary of the porosity after pressing in dependence on the factors A - carbonfiller type and B - maximum particle size as well as on their interaction


A 3 64 21.4 37.71 <2e-16 ***

B 2 4379 2189.7 3859.96 <2e-16 ***

A:B 6 133 22.1 39.02 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Tab. A.37.: ANOVA summary of the linear change in length of the samples after the pyrolysis in depen-dence on the factors A - carbon filler type and B - maximum particle size as well as on their interaction


A 3 2.2964 0.7655 90.224 <2e-16 ***

B 2 1.9285 0.9642 113.652 <2e-16 ***

A:B 6 0.1147 0.0191 2.254 0.0435 *

Residuals 107 0.9078 0.0085

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



Tab. A.38.: ANOVA summary of the porosity after the pressing in dependence on the factor A -Carbores® content


A 3 2300.1 766.7 528.5 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.39.: Results of the Tukey range test with a p-value of 0.05 for the influence of the differentCarbores® contents on the apparent porosity after the pressing; the values tested were evaluated atroom temperature, p < 0.05 indicates significant differences between the tested pair

Tukey multiple comparisons of means

95% family-wise confidence level

Fit: aov(formula = AP ~ A, data = joern.charge1)

$A

diff lwr upr p adj

10-5 -1.455455 -2.799121 -0.111788 0.0291863

20-5 -5.950000 -7.264132 -4.635868 0.0000000

30-5 -17.718333 -19.032465 -16.404202 0.0000000

20-10 -4.494545 -5.838212 -3.150879 0.0000000

30-10 -16.262879 -17.606545 -14.919212 0.0000000

30-20 -11.768333 -13.082465 -10.454202 0.0000000

A.1.3. Young’s modulus of carbon-bonded open cell foam structures

134 A. Appendix

Tab. A.40.: ANOVA summary of the porosity after the pyrolysis in dependence on the factor A -Carbores® content


A 3 503.4 167.79 775.7 <2e-16 ***


---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Tab. A.41.: Results of the Tukey range test with a p-value of 0.05 for the influence of the differentCarbores® contents on the porosity after the pyrolysis; the values tested were evaluated at room tem-perature, p < 0.05 indicates significant differences between the tested pair

Tukey multiple comparisons of means

95% family-wise confidence level

Fit: aov(formula = AP1 ~ A, data = joern.charge1)

$A

diff lwr upr p adj

10-5 -2.554865 -3.115033 -1.994697 0

20-5 -6.380383 -6.940551 -5.820215 0

30-5 -9.272631 -9.832799 -8.712462 0

20-10 -3.825518 -4.385686 -3.265350 0

30-10 -6.717766 -7.277934 -6.157598 0

30-20 -2.892248 -3.452416 -2.332080 0

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The in uence of composition, processing and temperature on